LMFDB - Embedded newform 105.3.l.a.43.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(22,105)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("105.22");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.10
Character	$\chi$	$=$	105.43
Dual form			105.3.l.a.22.10

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.24469 - 2.24469i) q^{2} +(1.22474 + 1.22474i) q^{3} -6.07726i q^{4} +(-3.05058 - 3.96156i) q^{5} +5.49834 q^{6} +(1.87083 - 1.87083i) q^{7} +(-4.66280 - 4.66280i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(2.24469 - 2.24469i) q^{2} +(1.22474 + 1.22474i) q^{3} -6.07726i q^{4} +(-3.05058 - 3.96156i) q^{5} +5.49834 q^{6} +(1.87083 - 1.87083i) q^{7} +(-4.66280 - 4.66280i) q^{8} +3.00000i q^{9} +(-15.7401 - 2.04487i) q^{10} +3.94671 q^{11} +(7.44309 - 7.44309i) q^{12} +(8.57045 + 8.57045i) q^{13} -8.39886i q^{14} +(1.11572 - 8.58808i) q^{15} +3.37595 q^{16} +(-17.2039 + 17.2039i) q^{17} +(6.73407 + 6.73407i) q^{18} +24.3758i q^{19} +(-24.0754 + 18.5392i) q^{20} +4.58258 q^{21} +(8.85913 - 8.85913i) q^{22} +(-19.6705 - 19.6705i) q^{23} -11.4215i q^{24} +(-6.38793 + 24.1701i) q^{25} +38.4760 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-11.3695 - 11.3695i) q^{28} -17.5580i q^{29} +(-16.7731 - 21.7820i) q^{30} -43.8736 q^{31} +(26.2292 - 26.2292i) q^{32} +(4.83371 + 4.83371i) q^{33} +77.2348i q^{34} +(-13.1185 - 1.70429i) q^{35} +18.2318 q^{36} +(32.9598 - 32.9598i) q^{37} +(54.7160 + 54.7160i) q^{38} +20.9932i q^{39} +(-4.24773 + 32.6962i) q^{40} +22.4582 q^{41} +(10.2865 - 10.2865i) q^{42} +(14.3533 + 14.3533i) q^{43} -23.9852i q^{44} +(11.8847 - 9.15174i) q^{45} -88.3085 q^{46} +(38.7355 - 38.7355i) q^{47} +(4.13468 + 4.13468i) q^{48} -7.00000i q^{49} +(39.9155 + 68.5933i) q^{50} -42.1407 q^{51} +(52.0849 - 52.0849i) q^{52} +(9.01352 + 9.01352i) q^{53} +16.4950i q^{54} +(-12.0397 - 15.6351i) q^{55} -17.4466 q^{56} +(-29.8541 + 29.8541i) q^{57} +(-39.4121 - 39.4121i) q^{58} -58.0335i q^{59} +(-52.1920 - 6.78052i) q^{60} -89.2995 q^{61} +(-98.4827 + 98.4827i) q^{62} +(5.61249 + 5.61249i) q^{63} -104.249i q^{64} +(7.80752 - 60.0972i) q^{65} +21.7004 q^{66} +(-21.2058 + 21.2058i) q^{67} +(104.552 + 104.552i) q^{68} -48.1828i q^{69} +(-33.2726 + 25.6214i) q^{70} -78.8147 q^{71} +(13.9884 - 13.9884i) q^{72} +(-18.2694 - 18.2694i) q^{73} -147.969i q^{74} +(-37.4258 + 21.7786i) q^{75} +148.138 q^{76} +(7.38362 - 7.38362i) q^{77} +(47.1233 + 47.1233i) q^{78} +112.267i q^{79} +(-10.2986 - 13.3740i) q^{80} -9.00000 q^{81} +(50.4118 - 50.4118i) q^{82} +(-12.9380 - 12.9380i) q^{83} -27.8495i q^{84} +(120.636 + 15.6724i) q^{85} +64.4373 q^{86} +(21.5040 - 21.5040i) q^{87} +(-18.4027 - 18.4027i) q^{88} -22.2193i q^{89} +(6.13461 - 47.2202i) q^{90} +32.0677 q^{91} +(-119.543 + 119.543i) q^{92} +(-53.7340 - 53.7340i) q^{93} -173.898i q^{94} +(96.5661 - 74.3602i) q^{95} +64.2481 q^{96} +(90.6427 - 90.6427i) q^{97} +(-15.7128 - 15.7128i) q^{98} +11.8401i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} + 16 q^{5} + 24 q^{6} - 48 q^{8}+O(q^{10}) $ 24 * q + 8 * q^2 + 16 * q^5 + 24 * q^6 - 48 * q^8	$ 24 q + 8 q^{2} + 16 q^{5} + 24 q^{6} - 48 q^{8} - 40 q^{10} - 48 q^{12} + 64 q^{13} - 184 q^{16} + 24 q^{17} + 24 q^{18} + 72 q^{20} + 8 q^{22} + 8 q^{23} - 136 q^{25} - 80 q^{26} + 96 q^{30} + 96 q^{31} + 56 q^{32} - 72 q^{33} + 168 q^{36} + 8 q^{37} + 56 q^{38} + 232 q^{40} + 320 q^{41} - 112 q^{43} - 72 q^{45} + 320 q^{46} + 64 q^{47} + 192 q^{48} - 256 q^{50} - 192 q^{51} + 96 q^{52} - 72 q^{53} - 80 q^{55} - 336 q^{56} + 48 q^{57} - 512 q^{58} - 192 q^{60} - 496 q^{61} - 776 q^{62} + 312 q^{65} - 192 q^{66} - 192 q^{67} + 568 q^{68} + 112 q^{70} - 144 q^{71} + 144 q^{72} + 224 q^{73} + 144 q^{75} + 416 q^{76} + 112 q^{77} - 216 q^{78} - 528 q^{80} - 216 q^{81} + 352 q^{82} - 32 q^{83} + 24 q^{85} + 240 q^{86} + 384 q^{87} + 216 q^{88} - 24 q^{90} + 1304 q^{92} + 376 q^{95} + 168 q^{96} - 816 q^{97} - 56 q^{98}+O(q^{100}) $ 24 * q + 8 * q^2 + 16 * q^5 + 24 * q^6 - 48 * q^8 - 40 * q^10 - 48 * q^12 + 64 * q^13 - 184 * q^16 + 24 * q^17 + 24 * q^18 + 72 * q^20 + 8 * q^22 + 8 * q^23 - 136 * q^25 - 80 * q^26 + 96 * q^30 + 96 * q^31 + 56 * q^32 - 72 * q^33 + 168 * q^36 + 8 * q^37 + 56 * q^38 + 232 * q^40 + 320 * q^41 - 112 * q^43 - 72 * q^45 + 320 * q^46 + 64 * q^47 + 192 * q^48 - 256 * q^50 - 192 * q^51 + 96 * q^52 - 72 * q^53 - 80 * q^55 - 336 * q^56 + 48 * q^57 - 512 * q^58 - 192 * q^60 - 496 * q^61 - 776 * q^62 + 312 * q^65 - 192 * q^66 - 192 * q^67 + 568 * q^68 + 112 * q^70 - 144 * q^71 + 144 * q^72 + 224 * q^73 + 144 * q^75 + 416 * q^76 + 112 * q^77 - 216 * q^78 - 528 * q^80 - 216 * q^81 + 352 * q^82 - 32 * q^83 + 24 * q^85 + 240 * q^86 + 384 * q^87 + 216 * q^88 - 24 * q^90 + 1304 * q^92 + 376 * q^95 + 168 * q^96 - 816 * q^97 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.24469	−	2.24469i	1.12234	−	1.12234i	0.130957	−	0.991388i	$-0.458195\pi$
$2$	2.24469	−	2.24469i	1.12234	−	1.12234i	0.991388	−	0.130957i	$-0.0418048\pi$
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$4$		−	6.07726i		−	1.51932i
$5$	−3.05058	−	3.96156i	−0.610116	−	0.792312i
$5$	−3.05058	−	3.96156i	−0.610116	−	0.792312i
$6$	5.49834			0.916391
$7$	1.87083	−	1.87083i	0.267261	−	0.267261i
$7$	1.87083	−	1.87083i	0.267261	−	0.267261i
$8$	−4.66280	−	4.66280i	−0.582850	−	0.582850i
$9$			3.00000i			0.333333i
$10$	−15.7401	−	2.04487i	−1.57401	−	0.204487i
$11$	3.94671			0.358792			0.179396	−	0.983777i	$-0.442586\pi$
$11$	3.94671			0.358792			0.179396	+	0.983777i	$0.442586\pi$
$12$	7.44309	−	7.44309i	0.620258	−	0.620258i
$13$	8.57045	+	8.57045i	0.659265	+	0.659265i	0.955206	−	0.295941i	$-0.0956331\pi$
$13$	8.57045	+	8.57045i	0.659265	+	0.659265i	−0.295941	+	0.955206i	$0.595633\pi$
$14$		−	8.39886i		−	0.599918i
$15$	1.11572	−	8.58808i	0.0743814	−	0.572539i
$16$	3.37595			0.210997
$17$	−17.2039	+	17.2039i	−1.01199	+	1.01199i	−0.0120660	+	0.999927i	$0.503841\pi$
$17$	−17.2039	+	17.2039i	−1.01199	+	1.01199i	−0.999927	+	0.0120660i	$0.996159\pi$
$18$	6.73407	+	6.73407i	0.374115	+	0.374115i
$19$			24.3758i			1.28294i	0.767150	+	0.641468i	$0.221674\pi$
$19$			24.3758i			1.28294i	−0.767150	+	0.641468i	$0.778326\pi$
$20$	−24.0754	+	18.5392i	−1.20377	+	0.926958i
$21$	4.58258			0.218218
$22$	8.85913	−	8.85913i	0.402688	−	0.402688i
$23$	−19.6705	−	19.6705i	−0.855240	−	0.855240i	0.135533	−	0.990773i	$-0.456725\pi$
$23$	−19.6705	−	19.6705i	−0.855240	−	0.855240i	−0.990773	+	0.135533i	$0.956725\pi$
$24$		−	11.4215i		−	0.475895i
$25$	−6.38793	+	24.1701i	−0.255517	+	0.966804i
$26$	38.4760			1.47985
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	−11.3695	−	11.3695i	−0.406054	−	0.406054i
$29$		−	17.5580i		−	0.605447i	−0.953078	−	0.302723i	$-0.902104\pi$
$29$		−	17.5580i		−	0.605447i	0.953078	−	0.302723i	$-0.0978958\pi$
$30$	−16.7731	−	21.7820i	−0.559104	−	0.726067i
$31$	−43.8736			−1.41528			−0.707639	−	0.706574i	$-0.750240\pi$
$31$	−43.8736			−1.41528			−0.707639	+	0.706574i	$0.750240\pi$
$32$	26.2292	−	26.2292i	0.819662	−	0.819662i
$33$	4.83371	+	4.83371i	0.146476	+	0.146476i
$34$			77.2348i			2.27161i
$35$	−13.1185	−	1.70429i	−0.374815	−	0.0486940i
$36$	18.2318			0.506438
$37$	32.9598	−	32.9598i	0.890805	−	0.890805i	−0.103794	−	0.994599i	$-0.533098\pi$
$37$	32.9598	−	32.9598i	0.890805	−	0.890805i	0.994599	+	0.103794i	$0.0330981\pi$
$38$	54.7160	+	54.7160i	1.43990	+	1.43990i
$39$			20.9932i			0.538288i
$40$	−4.24773	+	32.6962i	−0.106193	+	0.817406i
$41$	22.4582			0.547762			0.273881	−	0.961764i	$-0.411693\pi$
$41$	22.4582			0.547762			0.273881	+	0.961764i	$0.411693\pi$
$42$	10.2865	−	10.2865i	0.244916	−	0.244916i
$43$	14.3533	+	14.3533i	0.333797	+	0.333797i	0.854026	−	0.520230i	$-0.174154\pi$
$43$	14.3533	+	14.3533i	0.333797	+	0.333797i	−0.520230	+	0.854026i	$0.674154\pi$
$44$		−	23.9852i		−	0.545118i
$45$	11.8847	−	9.15174i	0.264104	−	0.203372i
$46$	−88.3085			−1.91975
$47$	38.7355	−	38.7355i	0.824159	−	0.824159i	−0.162542	−	0.986702i	$-0.551969\pi$
$47$	38.7355	−	38.7355i	0.824159	−	0.824159i	0.986702	+	0.162542i	$0.0519693\pi$
$48$	4.13468	+	4.13468i	0.0861391	+	0.0861391i
$49$		−	7.00000i		−	0.142857i
$50$	39.9155	+	68.5933i	0.798309	+	1.37187i
$51$	−42.1407			−0.826289
$52$	52.0849	−	52.0849i	1.00163	−	1.00163i
$53$	9.01352	+	9.01352i	0.170067	+	0.170067i	0.787009	−	0.616942i	$-0.211629\pi$
$53$	9.01352	+	9.01352i	0.170067	+	0.170067i	−0.616942	+	0.787009i	$0.711629\pi$
$54$			16.4950i			0.305464i
$55$	−12.0397	−	15.6351i	−0.218905	−	0.284275i
$56$	−17.4466			−0.311547
$57$	−29.8541	+	29.8541i	−0.523756	+	0.523756i
$58$	−39.4121	−	39.4121i	−0.679520	−	0.679520i
$59$		−	58.0335i		−	0.983618i	−0.870703	−	0.491809i	$-0.836336\pi$
$59$		−	58.0335i		−	0.983618i	0.870703	−	0.491809i	$-0.163664\pi$
$60$	−52.1920	−	6.78052i	−0.869867	−	0.113009i
$61$	−89.2995			−1.46393			−0.731963	−	0.681344i	$-0.761396\pi$
$61$	−89.2995			−1.46393			−0.731963	+	0.681344i	$0.761396\pi$
$62$	−98.4827	+	98.4827i	−1.58843	+	1.58843i
$63$	5.61249	+	5.61249i	0.0890871	+	0.0890871i
$64$		−	104.249i		−	1.62889i
$65$	7.80752	−	60.0972i	0.120116	−	0.924572i
$66$	21.7004			0.328793
$67$	−21.2058	+	21.2058i	−0.316505	+	0.316505i	−0.847423	−	0.530918i	$-0.821847\pi$
$67$	−21.2058	+	21.2058i	−0.316505	+	0.316505i	0.530918	+	0.847423i	$0.321847\pi$
$68$	104.552	+	104.552i	1.53754	+	1.53754i
$69$		−	48.1828i		−	0.698301i
$70$	−33.2726	+	25.6214i	−0.475323	+	0.366020i
$71$	−78.8147			−1.11007			−0.555033	−	0.831828i	$-0.687294\pi$
$71$	−78.8147			−1.11007			−0.555033	+	0.831828i	$0.687294\pi$
$72$	13.9884	−	13.9884i	0.194283	−	0.194283i
$73$	−18.2694	−	18.2694i	−0.250266	−	0.250266i	0.570814	−	0.821080i	$-0.306628\pi$
$73$	−18.2694	−	18.2694i	−0.250266	−	0.250266i	−0.821080	+	0.570814i	$0.806628\pi$
$74$		−	147.969i		−	1.99958i
$75$	−37.4258	+	21.7786i	−0.499011	+	0.290382i
$76$	148.138			1.94918
$77$	7.38362	−	7.38362i	0.0958911	−	0.0958911i
$78$	47.1233	+	47.1233i	0.604145	+	0.604145i
$79$			112.267i			1.42110i	0.703646	+	0.710551i	$0.251554\pi$
$79$			112.267i			1.42110i	−0.703646	+	0.710551i	$0.748446\pi$
$80$	−10.2986	−	13.3740i	−0.128732	−	0.167175i
$81$	−9.00000			−0.111111
$82$	50.4118	−	50.4118i	0.614777	−	0.614777i
$83$	−12.9380	−	12.9380i	−0.155879	−	0.155879i	0.624859	−	0.780738i	$-0.285157\pi$
$83$	−12.9380	−	12.9380i	−0.155879	−	0.155879i	−0.780738	+	0.624859i	$0.785157\pi$
$84$		−	27.8495i		−	0.331542i
$85$	120.636	+	15.6724i	1.41925	+	0.184382i
$86$	64.4373			0.749270
$87$	21.5040	−	21.5040i	0.247173	−	0.247173i
$88$	−18.4027	−	18.4027i	−0.209122	−	0.209122i
$89$		−	22.2193i		−	0.249655i	−0.992178	−	0.124827i	$-0.960162\pi$
$89$		−	22.2193i		−	0.249655i	0.992178	−	0.124827i	$-0.0398377\pi$
$90$	6.13461	−	47.2202i	0.0681624	−	0.524669i
$91$	32.0677			0.352392
$92$	−119.543	+	119.543i	−1.29938	+	1.29938i
$93$	−53.7340	−	53.7340i	−0.577785	−	0.577785i
$94$		−	173.898i		−	1.84998i
$95$	96.5661	−	74.3602i	1.01649	−	0.782739i
$96$	64.2481			0.669251
$97$	90.6427	−	90.6427i	0.934461	−	0.934461i	−0.0635195	−	0.997981i	$-0.520233\pi$
$97$	90.6427	−	90.6427i	0.934461	−	0.934461i	0.997981	+	0.0635195i	$0.0202325\pi$
$98$	−15.7128	−	15.7128i	−0.160335	−	0.160335i
$99$			11.8401i			0.119597i
$100$	146.888	+	38.8211i	1.46888	+	0.388211i
$101$	−180.124			−1.78341			−0.891703	−	0.452621i	$-0.850489\pi$
$101$	−180.124			−1.78341			−0.891703	+	0.452621i	$0.850489\pi$
$102$	−94.5929	+	94.5929i	−0.927381	+	0.927381i
$103$	137.374	+	137.374i	1.33373	+	1.33373i	0.902003	+	0.431729i	$0.142096\pi$
$103$	137.374	+	137.374i	1.33373	+	1.33373i	0.431729	+	0.902003i	$0.357904\pi$
$104$		−	79.9247i		−	0.768506i
$105$	−13.9795	−	18.1542i	−0.133138	−	0.172897i
$106$	40.4651			0.381746
$107$	−102.254	+	102.254i	−0.955648	+	0.955648i	−0.999057	−	0.0434091i	$-0.986178\pi$
$107$	−102.254	+	102.254i	−0.955648	+	0.955648i	0.0434091	+	0.999057i	$0.486178\pi$
$108$	22.3293	+	22.3293i	0.206753	+	0.206753i
$109$		−	58.4672i		−	0.536396i	−0.963364	−	0.268198i	$-0.913572\pi$
$109$		−	58.4672i		−	0.536396i	0.963364	−	0.268198i	$-0.0864282\pi$
$110$	−62.1215	−	8.07051i	−0.564741	−	0.0733683i
$111$	80.7347			0.727340
$112$	6.31582	−	6.31582i	0.0563913	−	0.0563913i
$113$	39.8190	+	39.8190i	0.352381	+	0.352381i	0.860995	−	0.508614i	$-0.169842\pi$
$113$	39.8190	+	39.8190i	0.352381	+	0.352381i	−0.508614	+	0.860995i	$0.669842\pi$
$114$			134.026i			1.17567i
$115$	−17.9195	+	137.933i	−0.155822	+	1.19941i
$116$	−106.704			−0.919864
$117$	−25.7113	+	25.7113i	−0.219755	+	0.219755i
$118$	−130.267	−	130.267i	−1.10396	−	1.10396i
$119$			64.3710i			0.540933i
$120$	−45.2469	+	34.8422i	−0.377058	+	0.290351i
$121$	−105.423			−0.871269
$122$	−200.450	+	200.450i	−1.64303	+	1.64303i
$123$	27.5056	+	27.5056i	0.223623	+	0.223623i
$124$			266.631i			2.15025i
$125$	115.238	−	48.4267i	0.921906	−	0.387413i
$126$	25.1966			0.199973
$127$	28.1517	−	28.1517i	0.221667	−	0.221667i	−0.587533	−	0.809200i	$-0.699901\pi$
$127$	28.1517	−	28.1517i	0.221667	−	0.221667i	0.809200	+	0.587533i	$0.199901\pi$
$128$	−129.090	−	129.090i	−1.00851	−	1.00851i
$129$			35.1582i			0.272544i
$130$	−117.374	−	152.425i	−0.902877	−	1.17250i
$131$	−32.5463			−0.248445			−0.124223	−	0.992254i	$-0.539644\pi$
$131$	−32.5463			−0.248445			−0.124223	+	0.992254i	$0.539644\pi$
$132$	29.3757	−	29.3757i	0.222543	−	0.222543i
$133$	45.6029	+	45.6029i	0.342879	+	0.342879i
$134$			95.2009i			0.710454i
$135$	25.7642	+	3.34716i	0.190846	+	0.0247938i
$136$	160.437			1.17968
$137$	184.159	−	184.159i	1.34423	−	1.34423i	0.452422	−	0.891804i	$-0.350560\pi$
$137$	184.159	−	184.159i	1.34423	−	1.34423i	0.891804	−	0.452422i	$-0.149440\pi$
$138$	−108.155	−	108.155i	−0.783734	−	0.783734i
$139$			76.2552i			0.548599i	0.961644	+	0.274299i	$0.0884459\pi$
$139$			76.2552i			0.548599i	−0.961644	+	0.274299i	$0.911554\pi$
$140$	−10.3574	+	79.7246i	−0.0739816	+	0.569462i
$141$	94.8822			0.672923
$142$	−176.914	+	176.914i	−1.24588	+	1.24588i
$143$	33.8251	+	33.8251i	0.236539	+	0.236539i
$144$			10.1278i			0.0703323i
$145$	−69.5569	+	53.5619i	−0.479703	+	0.369393i
$146$	−82.0184			−0.561770
$147$	8.57321	−	8.57321i	0.0583212	−	0.0583212i
$148$	−200.305	−	200.305i	−1.35341	−	1.35341i
$149$			232.403i			1.55975i	0.625933	+	0.779877i	$0.284718\pi$
$149$			232.403i			1.55975i	−0.625933	+	0.779877i	$0.715282\pi$
$150$	−35.1231	+	132.896i	−0.234154	+	0.885971i
$151$	170.930			1.13199			0.565994	−	0.824409i	$-0.308492\pi$
$151$	170.930			1.13199			0.565994	+	0.824409i	$0.308492\pi$
$152$	113.659	−	113.659i	0.747760	−	0.747760i
$153$	−51.6117	−	51.6117i	−0.337331	−	0.337331i
$154$		−	33.1478i		−	0.215246i
$155$	133.840	+	173.808i	0.863484	+	1.12134i
$156$	127.581			0.817829
$157$	199.875	−	199.875i	1.27309	−	1.27309i	0.328635	−	0.944457i	$-0.393411\pi$
$157$	199.875	−	199.875i	1.27309	−	1.27309i	0.944457	−	0.328635i	$-0.106589\pi$
$158$	252.005	+	252.005i	1.59497	+	1.59497i
$159$			22.0785i			0.138859i
$160$	−183.923	−	23.8943i	−1.14952	−	0.149339i
$161$	−73.6004			−0.457145
$162$	−20.2022	+	20.2022i	−0.124705	+	0.124705i
$163$	−147.090	−	147.090i	−0.902392	−	0.902392i	0.0932506	−	0.995643i	$-0.470274\pi$
$163$	−147.090	−	147.090i	−0.902392	−	0.902392i	−0.995643	+	0.0932506i	$0.970274\pi$
$164$		−	136.485i		−	0.832223i
$165$	4.40342	−	33.8947i	0.0266874	−	0.205422i
$166$	−58.0834			−0.349900
$167$	43.6355	−	43.6355i	0.261290	−	0.261290i	−0.564288	−	0.825578i	$-0.690849\pi$
$167$	43.6355	−	43.6355i	0.261290	−	0.261290i	0.825578	+	0.564288i	$0.190849\pi$
$168$	−21.3677	−	21.3677i	−0.127188	−	0.127188i
$169$		−	22.0948i		−	0.130738i
$170$	305.970	−	235.611i	1.79982	−	1.38595i
$171$	−73.1273			−0.427645
$172$	87.2285	−	87.2285i	0.507143	−	0.507143i
$173$	−79.6322	−	79.6322i	−0.460302	−	0.460302i	0.438453	−	0.898754i	$-0.355527\pi$
$173$	−79.6322	−	79.6322i	−0.460302	−	0.460302i	−0.898754	+	0.438453i	$0.855527\pi$
$174$		−	96.5397i		−	0.554826i
$175$	33.2674	+	57.1689i	0.190099	+	0.326679i
$176$	13.3239			0.0757039
$177$	71.0762	−	71.0762i	0.401560	−	0.401560i
$178$	−49.8754	−	49.8754i	−0.280199	−	0.280199i
$179$			189.993i			1.06141i	0.847555	+	0.530707i	$0.178074\pi$
$179$			189.993i			1.06141i	−0.847555	+	0.530707i	$0.821926\pi$
$180$	−55.6175	−	72.2263i	−0.308986	−	0.401257i
$181$	193.279			1.06784			0.533920	−	0.845535i	$-0.320718\pi$
$181$	193.279			1.06784			0.533920	+	0.845535i	$0.320718\pi$
$182$	71.9820	−	71.9820i	0.395505	−	0.395505i
$183$	−109.369	−	109.369i	−0.597646	−	0.597646i
$184$			183.440i			0.996955i
$185$	−231.119	−	30.0258i	−1.24929	−	0.162302i
$186$	−241.232			−1.29695
$187$	−67.8987	+	67.8987i	−0.363095	+	0.363095i
$188$	−235.406	−	235.406i	−1.25216	−	1.25216i
$189$			13.7477i			0.0727393i
$190$	49.8453	−	383.677i	0.262344	−	2.01935i
$191$	236.062			1.23593			0.617963	−	0.786207i	$-0.287958\pi$
$191$	236.062			1.23593			0.617963	+	0.786207i	$0.287958\pi$
$192$	127.678	−	127.678i	0.664991	−	0.664991i
$193$	126.994	+	126.994i	0.658001	+	0.658001i	0.954907	−	0.296906i	$-0.0959548\pi$
$193$	126.994	+	126.994i	0.658001	+	0.658001i	−0.296906	+	0.954907i	$0.595955\pi$
$194$		−	406.930i		−	2.09757i
$195$	83.1660	−	64.0415i	0.426492	−	0.328418i
$196$	−42.5408			−0.217045
$197$	123.086	−	123.086i	0.624804	−	0.624804i	−0.321952	−	0.946756i	$-0.604339\pi$
$197$	123.086	−	123.086i	0.624804	−	0.624804i	0.946756	+	0.321952i	$0.104339\pi$
$198$	26.5774	+	26.5774i	0.134229	+	0.134229i
$199$			27.6913i			0.139152i	0.997577	+	0.0695761i	$0.0221647\pi$
$199$			27.6913i			0.139152i	−0.997577	+	0.0695761i	$0.977835\pi$
$200$	142.486	−	82.9148i	0.712431	−	0.414574i
$201$	−51.9434			−0.258425
$202$	−404.322	+	404.322i	−2.00160	+	2.00160i
$203$	−32.8479	−	32.8479i	−0.161812	−	0.161812i
$204$			256.100i			1.25539i
$205$	−68.5106	−	88.9697i	−0.334198	−	0.433998i
$206$	616.726			2.99381
$207$	59.0116	−	59.0116i	0.285080	−	0.285080i
$208$	28.9334	+	28.9334i	0.139103	+	0.139103i
$209$			96.2041i			0.460307i
$210$	−72.1301	−	9.37078i	−0.343477	−	0.0446228i
$211$	−171.536			−0.812965			−0.406483	−	0.913658i	$-0.633245\pi$
$211$	−171.536			−0.812965			−0.406483	+	0.913658i	$0.633245\pi$
$212$	54.7775	−	54.7775i	0.258385	−	0.258385i
$213$	−96.5278	−	96.5278i	−0.453182	−	0.453182i
$214$			459.059i			2.14513i
$215$	13.0756	−	100.647i	0.0608166	−	0.468126i
$216$	34.2645			0.158632
$217$	−82.0801	+	82.0801i	−0.378249	+	0.378249i
$218$	−131.241	−	131.241i	−0.602021	−	0.602021i
$219$		−	44.7508i		−	0.204341i
$220$	−95.0187	+	73.1687i	−0.431903	+	0.332585i
$221$	−294.890			−1.33434
$222$	181.224	−	181.224i	0.816326	−	0.816326i
$223$	6.27227	+	6.27227i	0.0281268	+	0.0281268i	0.721030	−	0.692904i	$-0.243669\pi$
$223$	6.27227	+	6.27227i	0.0281268	+	0.0281268i	−0.692904	+	0.721030i	$0.743669\pi$
$224$		−	98.1406i		−	0.438128i
$225$	−72.5103	−	19.1638i	−0.322268	−	0.0851724i
$226$	178.763			0.790985
$227$	−155.382	+	155.382i	−0.684501	+	0.684501i	−0.961011	−	0.276510i	$-0.910822\pi$
$227$	−155.382	+	155.382i	−0.684501	+	0.684501i	0.276510	+	0.961011i	$0.410822\pi$
$228$	181.431	+	181.431i	0.795751	+	0.795751i
$229$		−	283.171i		−	1.23656i	−0.785960	−	0.618278i	$-0.787831\pi$
$229$		−	283.171i		−	1.23656i	0.785960	−	0.618278i	$-0.212169\pi$
$230$	269.392	+	349.839i	1.17127	+	1.52104i
$231$	18.0861			0.0782948
$232$	−81.8693	+	81.8693i	−0.352885	+	0.352885i
$233$	18.5950	+	18.5950i	0.0798069	+	0.0798069i	0.745883	−	0.666077i	$-0.232028\pi$
$233$	18.5950	+	18.5950i	0.0798069	+	0.0798069i	−0.666077	+	0.745883i	$0.732028\pi$
$234$			115.428i			0.493282i
$235$	−271.619	−	35.2873i	−1.15582	−	0.150159i
$236$	−352.684			−1.49443
$237$	−137.499	+	137.499i	−0.580162	+	0.580162i
$238$	144.493	+	144.493i	0.607113	+	0.607113i
$239$			265.031i			1.10892i	0.832211	+	0.554459i	$0.187075\pi$
$239$			265.031i			1.10892i	−0.832211	+	0.554459i	$0.812925\pi$
$240$	3.76662	−	28.9929i	0.0156942	−	0.120804i
$241$	127.492			0.529011			0.264506	−	0.964384i	$-0.414791\pi$
$241$	127.492			0.529011			0.264506	+	0.964384i	$0.414791\pi$
$242$	−236.643	+	236.643i	−0.977864	+	0.977864i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$			542.696i			2.22417i
$245$	−27.7309	+	21.3541i	−0.113187	+	0.0871594i
$246$	123.483			0.501964
$247$	−208.911	+	208.911i	−0.845795	+	0.845795i
$248$	204.574	+	204.574i	0.824896	+	0.824896i
$249$		−	31.6914i		−	0.127275i
$250$	149.971	−	367.377i	0.599885	−	1.46951i
$251$	31.9519			0.127298			0.0636492	−	0.997972i	$-0.479726\pi$
$251$	31.9519			0.127298			0.0636492	+	0.997972i	$0.479726\pi$
$252$	34.1085	−	34.1085i	0.135351	−	0.135351i
$253$	−77.6338	−	77.6338i	−0.306853	−	0.306853i
$254$		−	126.383i		−	0.497573i
$255$	128.554	+	166.943i	0.504132	+	0.654679i
$256$	−162.537			−0.634910
$257$	−138.387	+	138.387i	−0.538470	+	0.538470i	−0.923079	−	0.384610i	$-0.874336\pi$
$257$	−138.387	+	138.387i	−0.538470	+	0.538470i	0.384610	+	0.923079i	$0.374336\pi$
$258$	78.9192	+	78.9192i	0.305888	+	0.305888i
$259$		−	123.324i		−	0.476155i
$260$	−365.226	−	47.4484i	−1.40472	−	0.182494i
$261$	52.6739			0.201816
$262$	−73.0564	+	73.0564i	−0.278841	+	0.278841i
$263$	−230.486	−	230.486i	−0.876373	−	0.876373i	0.116785	−	0.993157i	$-0.462741\pi$
$263$	−230.486	−	230.486i	−0.876373	−	0.876373i	−0.993157	+	0.116785i	$0.962741\pi$
$264$		−	45.0773i		−	0.170747i
$265$	8.21116	−	63.2041i	0.0309855	−	0.238506i
$266$	204.729			0.769657
$267$	27.2129	−	27.2129i	0.101921	−	0.101921i
$268$	128.873	+	128.873i	0.480870	+	0.480870i
$269$		−	332.673i		−	1.23670i	−0.785901	−	0.618352i	$-0.787801\pi$
$269$		−	332.673i		−	1.23670i	0.785901	−	0.618352i	$-0.212199\pi$
$270$	65.3461	−	50.3194i	0.242022	−	0.186368i
$271$	−253.724			−0.936251			−0.468126	−	0.883662i	$-0.655071\pi$
$271$	−253.724			−0.936251			−0.468126	+	0.883662i	$0.655071\pi$
$272$	−58.0794	+	58.0794i	−0.213527	+	0.213527i
$273$	39.2747	+	39.2747i	0.143863	+	0.143863i
$274$		−	826.759i		−	3.01737i
$275$	−25.2113	+	95.3924i	−0.0916775	+	0.346881i
$276$	−292.819			−1.06094
$277$	252.491	−	252.491i	0.911521	−	0.911521i	−0.0848711	−	0.996392i	$-0.527048\pi$
$277$	252.491	−	252.491i	0.911521	−	0.911521i	0.996392	+	0.0848711i	$0.0270479\pi$
$278$	171.169	+	171.169i	0.615717	+	0.615717i
$279$		−	131.621i		−	0.471759i
$280$	53.2223	+	69.1158i	0.190080	+	0.246842i
$281$	−3.26524			−0.0116201			−0.00581004	−	0.999983i	$-0.501849\pi$
$281$	−3.26524			−0.0116201			−0.00581004	+	0.999983i	$0.501849\pi$
$282$	212.981	−	212.981i	0.755252	−	0.755252i
$283$	61.6256	+	61.6256i	0.217758	+	0.217758i	0.807553	−	0.589795i	$-0.200791\pi$
$283$	61.6256	+	61.6256i	0.217758	+	0.217758i	−0.589795	+	0.807553i	$0.700791\pi$
$284$			478.977i			1.68654i
$285$	209.341	+	27.1966i	0.734531	+	0.0954265i
$286$	151.854			0.530956
$287$	42.0155	−	42.0155i	0.146395	−	0.146395i
$288$	78.6875	+	78.6875i	0.273221	+	0.273221i
$289$		−	302.947i		−	1.04826i
$290$	−35.9038	+	276.364i	−0.123806	+	0.952978i
$291$	222.028			0.762984
$292$	−111.028	+	111.028i	−0.380233	+	0.380233i
$293$	150.796	+	150.796i	0.514663	+	0.514663i	0.915952	−	0.401289i	$-0.131438\pi$
$293$	150.796	+	150.796i	0.514663	+	0.514663i	−0.401289	+	0.915952i	$0.631438\pi$
$294$		−	38.4884i		−	0.130913i
$295$	−229.903	+	177.036i	−0.779332	+	0.600121i
$296$	−307.370			−1.03841
$297$	−14.5011	+	14.5011i	−0.0488254	+	0.0488254i
$298$	521.673	+	521.673i	1.75058	+	1.75058i
$299$		−	337.171i		−	1.12766i
$300$	132.354	+	227.446i	0.441181	+	0.758155i
$301$	53.7050			0.178422
$302$	383.685	−	383.685i	1.27048	−	1.27048i
$303$	−220.606	−	220.606i	−0.728072	−	0.728072i
$304$			82.2914i			0.270695i
$305$	272.415	+	353.766i	0.893165	+	1.15989i
$306$	−231.704			−0.757203
$307$	37.6731	−	37.6731i	0.122714	−	0.122714i	−0.643083	−	0.765797i	$-0.722345\pi$
$307$	37.6731	−	37.6731i	0.122714	−	0.122714i	0.765797	+	0.643083i	$0.222345\pi$
$308$	−44.8722	−	44.8722i	−0.145689	−	0.145689i
$309$			336.497i			1.08899i
$310$	690.574	+	89.7159i	2.22766	+	0.289406i
$311$	208.646			0.670888			0.335444	−	0.942060i	$-0.391114\pi$
$311$	208.646			0.670888			0.335444	+	0.942060i	$0.391114\pi$
$312$	97.8873	−	97.8873i	0.313741	−	0.313741i
$313$	−25.0439	−	25.0439i	−0.0800125	−	0.0800125i	0.665968	−	0.745980i	$-0.268019\pi$
$313$	−25.0439	−	25.0439i	−0.0800125	−	0.0800125i	−0.745980	+	0.665968i	$0.768019\pi$
$314$		−	897.316i		−	2.85770i
$315$	5.11287	−	39.3555i	0.0162313	−	0.124938i
$316$	682.276			2.15910
$317$	−164.900	+	164.900i	−0.520188	+	0.520188i	−0.917628	−	0.397440i	$-0.869899\pi$
$317$	−164.900	+	164.900i	−0.520188	+	0.520188i	0.397440	+	0.917628i	$0.369899\pi$
$318$	49.5595	+	49.5595i	0.155847	+	0.155847i
$319$		−	69.2961i		−	0.217229i
$320$	−412.988	+	318.019i	−1.29059	+	0.993811i
$321$	−250.471			−0.780284
$322$	−165.210	+	165.210i	−0.513074	+	0.513074i
$323$	−419.358	−	419.358i	−1.29832	−	1.29832i
$324$			54.6953i			0.168813i
$325$	−261.896	+	152.401i	−0.805834	+	0.468927i
$326$	−660.342			−2.02559
$327$	71.6074	−	71.6074i	0.218983	−	0.218983i
$328$	−104.718	−	104.718i	−0.319263	−	0.319263i
$329$		−	144.935i		−	0.440532i
$330$	−66.1987	−	85.9673i	−0.200602	−	0.260507i
$331$	−324.395			−0.980045			−0.490023	−	0.871710i	$-0.663011\pi$
$331$	−324.395			−0.980045			−0.490023	+	0.871710i	$0.663011\pi$
$332$	−78.6273	+	78.6273i	−0.236829	+	0.236829i
$333$	98.8794	+	98.8794i	0.296935	+	0.296935i
$334$		−	195.896i		−	0.586516i
$335$	148.698	+	19.3181i	0.443875	+	0.0576660i
$336$	15.4705			0.0460433
$337$	−27.1490	+	27.1490i	−0.0805607	+	0.0805607i	−0.746239	−	0.665678i	$-0.768142\pi$
$337$	−27.1490	+	27.1490i	−0.0805607	+	0.0805607i	0.665678	+	0.746239i	$0.268142\pi$
$338$	−49.5959	−	49.5959i	−0.146734	−	0.146734i
$339$			97.5362i			0.287718i
$340$	95.2454	−	733.137i	0.280134	−	2.15628i
$341$	−173.156			−0.507790
$342$	−164.148	+	164.148i	−0.479965	+	0.479965i
$343$	−13.0958	−	13.0958i	−0.0381802	−	0.0381802i
$344$		−	133.853i		−	0.389107i
$345$	−190.879	+	146.985i	−0.553272	+	0.426044i
$346$	−357.499			−1.03323
$347$	−0.188420	+	0.188420i	−0.000542997	+	0.000542997i	−0.707378	−	0.706835i	$-0.750122\pi$
$347$	−0.188420	+	0.188420i	−0.000542997	+	0.000542997i	0.706835	+	0.707378i	$0.250122\pi$
$348$	−130.685	−	130.685i	−0.375533	−	0.375533i
$349$		−	222.903i		−	0.638690i	−0.947638	−	0.319345i	$-0.896537\pi$
$349$		−	222.903i		−	0.638690i	0.947638	−	0.319345i	$-0.103463\pi$
$350$	203.001	+	53.6513i	0.580004	+	0.153290i
$351$	−62.9797			−0.179429
$352$	103.519	−	103.519i	0.294088	−	0.294088i
$353$	10.0036	+	10.0036i	0.0283387	+	0.0283387i	0.721134	−	0.692795i	$-0.243621\pi$
$353$	10.0036	+	10.0036i	0.0283387	+	0.0283387i	−0.692795	+	0.721134i	$0.743621\pi$
$354$		−	319.088i		−	0.901378i
$355$	240.430	+	312.229i	0.677269	+	0.879519i
$356$	−135.032			−0.379304
$357$	−78.8381	+	78.8381i	−0.220835	+	0.220835i
$358$	426.476	+	426.476i	1.19127	+	1.19127i
$359$			605.191i			1.68577i	0.538096	+	0.842884i	$0.319144\pi$
$359$			605.191i			1.68577i	−0.538096	+	0.842884i	$0.680856\pi$
$360$	−98.0887	−	12.7432i	−0.272469	−	0.0353978i
$361$	−233.179			−0.645924
$362$	433.851	−	433.851i	1.19848	−	1.19848i
$363$	−129.117	−	129.117i	−0.355694	−	0.355694i
$364$		−	194.884i		−	0.535395i
$365$	−16.6431	+	128.108i	−0.0455976	+	0.350980i
$366$	−490.999			−1.34153
$367$	259.533	−	259.533i	0.707174	−	0.707174i	−0.258766	−	0.965940i	$-0.583316\pi$
$367$	259.533	−	259.533i	0.707174	−	0.707174i	0.965940	+	0.258766i	$0.0833157\pi$
$368$	−66.4067	−	66.4067i	−0.180453	−	0.180453i
$369$			67.3747i			0.182587i
$370$	−586.188	+	451.391i	−1.58429	+	1.21998i
$371$	33.7255			0.0909044
$372$	−326.556	+	326.556i	−0.877837	+	0.877837i
$373$	446.882	+	446.882i	1.19807	+	1.19807i	0.974742	+	0.223332i	$0.0716934\pi$
$373$	446.882	+	446.882i	1.19807	+	1.19807i	0.223332	+	0.974742i	$0.428307\pi$
$374$			304.823i			0.815035i
$375$	200.448	+	81.8272i	0.534527	+	0.218206i
$376$	−361.232			−0.960724
$377$	150.480	−	150.480i	0.399150	−	0.399150i
$378$	30.8594	+	30.8594i	0.0816386	+	0.0816386i
$379$			51.1198i			0.134881i	0.997723	+	0.0674404i	$0.0214832\pi$
$379$			51.1198i			0.134881i	−0.997723	+	0.0674404i	$0.978517\pi$
$380$	−451.907	−	586.858i	−1.18923	−	1.54436i
$381$	68.9572			0.180990
$382$	529.886	−	529.886i	1.38714	−	1.38714i
$383$	405.345	+	405.345i	1.05834	+	1.05834i	0.998189	+	0.0601525i	$0.0191587\pi$
$383$	405.345	+	405.345i	1.05834	+	1.05834i	0.0601525	+	0.998189i	$0.480841\pi$
$384$		−	316.204i		−	0.823448i
$385$	−51.7750	−	6.72634i	−0.134480	−	0.0174710i
$386$	570.125			1.47701
$387$	−43.0598	+	43.0598i	−0.111266	+	0.111266i
$388$	−550.859	−	550.859i	−1.41974	−	1.41974i
$389$			47.3061i			0.121609i	0.998150	+	0.0608047i	$0.0193667\pi$
$389$			47.3061i			0.121609i	−0.998150	+	0.0608047i	$0.980633\pi$
$390$	42.9285	−	330.435i	0.110073	−	0.847269i
$391$	676.819			1.73099
$392$	−32.6396	+	32.6396i	−0.0832644	+	0.0832644i
$393$	−39.8610	−	39.8610i	−0.101427	−	0.101427i
$394$		−	552.581i		−	1.40249i
$395$	444.753	−	342.480i	1.12596	−	0.867037i
$396$	71.9555			0.181706
$397$	−338.755	+	338.755i	−0.853287	+	0.853287i	−0.990537	−	0.137249i	$-0.956174\pi$
$397$	−338.755	+	338.755i	−0.853287	+	0.853287i	0.137249	+	0.990537i	$0.456174\pi$
$398$	62.1583	+	62.1583i	0.156177	+	0.156177i
$399$			111.704i			0.279960i
$400$	−21.5653	+	81.5971i	−0.0539133	+	0.203993i
$401$	351.967			0.877723			0.438861	−	0.898555i	$-0.355382\pi$
$401$	351.967			0.877723			0.438861	+	0.898555i	$0.355382\pi$
$402$	−116.597	+	116.597i	−0.290042	+	0.290042i
$403$	−376.017	−	376.017i	−0.933044	−	0.933044i
$404$			1094.66i			2.70955i
$405$	27.4552	+	35.6541i	0.0677906	+	0.0880347i
$406$	−147.467			−0.363219
$407$	130.083	−	130.083i	0.319614	−	0.319614i
$408$	196.494	+	196.494i	0.481603	+	0.481603i
$409$		−	34.7110i		−	0.0848681i	−0.999099	−	0.0424340i	$-0.986489\pi$
$409$		−	34.7110i		−	0.0848681i	0.999099	−	0.0424340i	$-0.0135112\pi$
$410$	−353.494	−	45.9242i	−0.862181	−	0.112010i
$411$	451.096			1.09756
$412$	834.860	−	834.860i	2.02636	−	2.02636i
$413$	−108.571	−	108.571i	−0.262883	−	0.262883i
$414$		−	264.925i		−	0.639916i
$415$	−11.7862	+	90.7228i	−0.0284006	+	0.218609i
$416$	449.592			1.08075
$417$	−93.3932	+	93.3932i	−0.223964	+	0.223964i
$418$	215.948	+	215.948i	0.516623	+	0.516623i
$419$		−	522.337i		−	1.24663i	−0.781972	−	0.623313i	$-0.785786\pi$
$419$		−	522.337i		−	1.24663i	0.781972	−	0.623313i	$-0.214214\pi$
$420$	−110.328	+	84.9571i	−0.262685	+	0.202279i
$421$	150.337			0.357096			0.178548	−	0.983931i	$-0.442860\pi$
$421$	150.337			0.357096			0.178548	+	0.983931i	$0.442860\pi$
$422$	−385.044	+	385.044i	−0.912427	+	0.912427i
$423$	116.206	+	116.206i	0.274720	+	0.274720i
$424$		−	84.0566i		−	0.198247i
$425$	−305.923	−	525.717i	−0.719818	−	1.23698i
$426$	−433.350			−1.01725
$427$	−167.064	+	167.064i	−0.391251	+	0.391251i
$428$	621.426	+	621.426i	1.45193	+	1.45193i
$429$			82.8542i			0.193133i
$430$	−196.571	−	255.272i	−0.457142	−	0.593656i
$431$	−165.122			−0.383113			−0.191557	−	0.981482i	$-0.561354\pi$
$431$	−165.122			−0.383113			−0.191557	+	0.981482i	$0.561354\pi$
$432$	−12.4040	+	12.4040i	−0.0287130	+	0.0287130i
$433$	−173.796	−	173.796i	−0.401377	−	0.401377i	0.477341	−	0.878718i	$-0.341601\pi$
$433$	−173.796	−	173.796i	−0.401377	−	0.401377i	−0.878718	+	0.477341i	$0.841601\pi$
$434$			368.488i			0.849052i
$435$	−150.789	−	19.5898i	−0.346642	−	0.0450339i
$436$	−355.320			−0.814955
$437$	479.484	−	479.484i	1.09722	−	1.09722i
$438$	−100.452	−	100.452i	−0.229342	−	0.229342i
$439$		−	140.286i		−	0.319558i	−0.987153	−	0.159779i	$-0.948922\pi$
$439$		−	140.286i		−	0.319558i	0.987153	−	0.159779i	$-0.0510782\pi$
$440$	−16.7646	+	129.043i	−0.0381013	+	0.293278i
$441$	21.0000			0.0476190
$442$	−661.937	+	661.937i	−1.49759	+	1.49759i
$443$	548.196	+	548.196i	1.23746	+	1.23746i	0.961034	+	0.276429i	$0.0891511\pi$
$443$	548.196	+	548.196i	1.23746	+	1.23746i	0.276429	+	0.961034i	$0.410849\pi$
$444$		−	490.646i		−	1.10506i
$445$	−88.0230	+	67.7817i	−0.197805	+	0.152318i
$446$	28.1586			0.0631359
$447$	−284.635	+	284.635i	−0.636767	+	0.636767i
$448$	−195.032	−	195.032i	−0.435339	−	0.435339i
$449$			693.773i			1.54515i	0.634923	+	0.772576i	$0.281032\pi$
$449$			693.773i			1.54515i	−0.634923	+	0.772576i	$0.718968\pi$
$450$	−205.780	+	119.746i	−0.457289	+	0.266103i
$451$	88.6361			0.196532
$452$	241.990	−	241.990i	0.535377	−	0.535377i
$453$	209.346	+	209.346i	0.462132	+	0.462132i
$454$			697.568i			1.53649i
$455$	−97.8250	−	127.038i	−0.215000	−	0.279205i
$456$	278.408			0.610543
$457$	327.671	−	327.671i	0.717004	−	0.717004i	−0.250987	−	0.967990i	$-0.580755\pi$
$457$	327.671	−	327.671i	0.717004	−	0.717004i	0.967990	+	0.250987i	$0.0807551\pi$
$458$	−635.632	−	635.632i	−1.38784	−	1.38784i
$459$		−	126.422i		−	0.275430i
$460$	838.252	+	108.901i	1.82229	+	0.236742i
$461$	93.1493			0.202059			0.101030	−	0.994883i	$-0.467786\pi$
$461$	93.1493			0.202059			0.101030	+	0.994883i	$0.467786\pi$
$462$	40.5977	−	40.5977i	0.0878737	−	0.0878737i
$463$	−498.598	−	498.598i	−1.07689	−	1.07689i	−0.996787	−	0.0800990i	$-0.974476\pi$
$463$	−498.598	−	498.598i	−1.07689	−	1.07689i	−0.0800990	−	0.996787i	$-0.525524\pi$
$464$		−	59.2747i		−	0.127747i
$465$	−48.9507	+	376.790i	−0.105270	+	0.810302i
$466$	83.4800			0.179142
$467$	−308.256	+	308.256i	−0.660078	+	0.660078i	−0.955398	−	0.295320i	$-0.904574\pi$
$467$	−308.256	+	308.256i	−0.660078	+	0.660078i	0.295320	+	0.955398i	$0.404574\pi$
$468$	156.255	+	156.255i	0.333877	+	0.333877i
$469$			79.3449i			0.169179i
$470$	−688.909	+	530.491i	−1.46576	+	1.12870i
$471$	489.593			1.03948
$472$	−270.599	+	270.599i	−0.573302	+	0.573302i
$473$	56.6482	+	56.6482i	0.119764	+	0.119764i
$474$			617.283i			1.30228i
$475$	−589.165	−	155.711i	−1.24035	−	0.327812i
$476$	391.200			0.821848
$477$	−27.0406	+	27.0406i	−0.0566888	+	0.0566888i
$478$	594.913	+	594.913i	1.24459	+	1.24459i
$479$		−	178.073i		−	0.371760i	−0.982572	−	0.185880i	$-0.940486\pi$
$479$		−	178.073i		−	0.371760i	0.982572	−	0.185880i	$-0.0595136\pi$
$480$	−195.994	−	254.523i	−0.408321	−	0.530256i
$481$	564.961			1.17455
$482$	286.179	−	286.179i	0.593733	−	0.593733i
$483$	−90.1417	−	90.1417i	−0.186629	−	0.186629i
$484$			640.686i			1.32373i
$485$	−635.600	−	82.5739i	−1.31051	−	0.170255i
$486$	−49.4851			−0.101821
$487$	−330.361	+	330.361i	−0.678359	+	0.678359i	−0.959629	−	0.281270i	$-0.909244\pi$
$487$	−330.361	+	330.361i	−0.678359	+	0.678359i	0.281270	+	0.959629i	$0.409244\pi$
$488$	416.386	+	416.386i	0.853250	+	0.853250i
$489$		−	360.295i		−	0.736800i
$490$	−14.3141	+	110.181i	−0.0292124	+	0.224858i
$491$	−729.372			−1.48548			−0.742741	−	0.669578i	$-0.766475\pi$
$491$	−729.372			−1.48548			−0.742741	+	0.669578i	$0.766475\pi$
$492$	167.159	−	167.159i	0.339753	−	0.339753i
$493$	302.065	+	302.065i	0.612708	+	0.612708i
$494$			937.882i			1.89855i
$495$	46.9054	−	36.1192i	0.0947584	−	0.0729682i
$496$	−148.115			−0.298619
$497$	−147.449	+	147.449i	−0.296678	+	0.296678i
$498$	−71.1373	−	71.1373i	−0.142846	−	0.142846i
$499$		−	385.715i		−	0.772976i	−0.922294	−	0.386488i	$-0.873688\pi$
$499$		−	385.715i		−	0.772976i	0.922294	−	0.386488i	$-0.126312\pi$
$500$	−294.301	−	700.333i	−0.588603	−	1.40067i
$501$	106.885			0.213343
$502$	71.7220	−	71.7220i	0.142873	−	0.142873i
$503$	−139.070	−	139.070i	−0.276482	−	0.276482i	0.555221	−	0.831703i	$-0.312634\pi$
$503$	−139.070	−	139.070i	−0.276482	−	0.276482i	−0.831703	+	0.555221i	$0.812634\pi$
$504$		−	52.3398i		−	0.103849i
$505$	549.482	+	713.572i	1.08808	+	1.41301i
$506$	−348.528			−0.688790
$507$	27.0605	−	27.0605i	0.0533737	−	0.0533737i
$508$	−171.085	−	171.085i	−0.336781	−	0.336781i
$509$			337.164i			0.662404i	0.943560	+	0.331202i	$0.107454\pi$
$509$			337.164i			0.662404i	−0.943560	+	0.331202i	$0.892546\pi$
$510$	663.298	+	86.1724i	1.30059	+	0.168965i
$511$	−68.3579			−0.133773
$512$	151.514	−	151.514i	0.295926	−	0.295926i
$513$	−89.5623	−	89.5623i	−0.174585	−	0.174585i
$514$			621.270i			1.20870i
$515$	125.146	−	963.289i	0.243001	−	1.87046i
$516$	213.665			0.414080
$517$	152.878	−	152.878i	0.295702	−	0.295702i
$518$	−276.825	−	276.825i	−0.534411	−	0.534411i
$519$		−	195.058i		−	0.375835i
$520$	−316.626	+	243.816i	−0.608897	+	0.468878i
$521$	−346.121			−0.664340			−0.332170	−	0.943220i	$-0.607781\pi$
$521$	−346.121			−0.664340			−0.332170	+	0.943220i	$0.607781\pi$
$522$	118.236	−	118.236i	0.226507	−	0.226507i
$523$	−295.339	−	295.339i	−0.564702	−	0.564702i	0.365938	−	0.930639i	$-0.380748\pi$
$523$	−295.339	−	295.339i	−0.564702	−	0.564702i	−0.930639	+	0.365938i	$0.880748\pi$
$524$			197.793i			0.377467i
$525$	−29.2732	+	110.761i	−0.0557585	+	0.210974i
$526$	−1034.74			−1.96718
$527$	754.797	−	754.797i	1.43225	−	1.43225i
$528$	16.3184	+	16.3184i	0.0309060	+	0.0309060i
$529$			244.859i			0.462872i
$530$	−123.442	−	160.305i	−0.232910	−	0.302462i
$531$	174.100			0.327873
$532$	277.141	−	277.141i	0.520941	−	0.520941i
$533$	192.477	+	192.477i	0.361120	+	0.361120i
$534$		−	122.169i		−	0.228781i
$535$	717.022	+	93.1519i	1.34023	+	0.174116i
$536$	197.757			0.368950
$537$	−232.693	+	232.693i	−0.433321	+	0.433321i
$538$	−746.748	−	746.748i	−1.38801	−	1.38801i
$539$		−	27.6270i		−	0.0512560i
$540$	20.3416	−	156.576i	0.0376696	−	0.289956i
$541$	−734.168			−1.35706			−0.678529	−	0.734574i	$-0.737382\pi$
$541$	−734.168			−1.35706			−0.678529	+	0.734574i	$0.737382\pi$
$542$	−569.532	+	569.532i	−1.05080	+	1.05080i
$543$	236.718	+	236.718i	0.435944	+	0.435944i
$544$			902.487i			1.65898i
$545$	−231.621	+	178.359i	−0.424993	+	0.327264i
$546$	176.319			0.322929
$547$	124.027	−	124.027i	0.226740	−	0.226740i	−0.584589	−	0.811329i	$-0.698744\pi$
$547$	124.027	−	124.027i	0.226740	−	0.226740i	0.811329	+	0.584589i	$0.198744\pi$
$548$	−1119.18	−	1119.18i	−2.04230	−	2.04230i
$549$		−	267.899i		−	0.487976i
$550$	157.535	+	270.718i	0.286427	+	0.492214i
$551$	427.989			0.776749
$552$	−224.667	+	224.667i	−0.407005	+	0.407005i
$553$	210.032	+	210.032i	0.379805	+	0.379805i
$554$		−	1133.53i		−	2.04608i
$555$	−246.288	−	319.835i	−0.443761	−	0.576280i
$556$	463.423			0.833494
$557$	−436.412	+	436.412i	−0.783504	+	0.783504i	−0.980420	−	0.196916i	$-0.936907\pi$
$557$	−436.412	+	436.412i	−0.783504	+	0.783504i	0.196916	+	0.980420i	$0.436907\pi$
$558$	−295.448	−	295.448i	−0.529477	−	0.529477i
$559$			246.028i			0.440121i
$560$	−44.2874	−	5.75360i	−0.0790847	−	0.0102743i
$561$	−166.317			−0.296466
$562$	−7.32946	+	7.32946i	−0.0130417	+	0.0130417i
$563$	−259.609	−	259.609i	−0.461117	−	0.461117i	0.437905	−	0.899021i	$-0.355721\pi$
$563$	−259.609	−	259.609i	−0.461117	−	0.461117i	−0.899021	+	0.437905i	$0.855721\pi$
$564$		−	576.624i		−	1.02238i
$565$	36.2744	−	279.216i	0.0642025	−	0.494188i
$566$	276.661			0.488800
$567$	−16.8375	+	16.8375i	−0.0296957	+	0.0296957i
$568$	367.497	+	367.497i	0.647002	+	0.647002i
$569$		−	151.092i		−	0.265539i	−0.991147	−	0.132770i	$-0.957613\pi$
$569$		−	151.092i		−	0.265539i	0.991147	−	0.132770i	$-0.0423870\pi$
$570$	530.954	−	408.858i	0.931498	−	0.717295i
$571$	−502.406			−0.879871			−0.439935	−	0.898029i	$-0.644999\pi$
$571$	−502.406			−0.879871			−0.439935	+	0.898029i	$0.644999\pi$
$572$	205.564	−	205.564i	0.359377	−	0.359377i
$573$	289.116	+	289.116i	0.504565	+	0.504565i
$574$		−	188.624i		−	0.328612i
$575$	601.093	−	349.785i	1.04538	−	0.608321i
$576$	312.747			0.542963
$577$	81.3805	−	81.3805i	0.141041	−	0.141041i	−0.633061	−	0.774102i	$-0.718202\pi$
$577$	81.3805	−	81.3805i	0.141041	−	0.141041i	0.774102	+	0.633061i	$0.218202\pi$
$578$	−680.023	−	680.023i	−1.17651	−	1.17651i
$579$			311.071i			0.537255i
$580$	325.510	+	422.715i	0.561224	+	0.728820i
$581$	−48.4094			−0.0833208
$582$	498.385	−	498.385i	0.856331	−	0.856331i
$583$	35.5738	+	35.5738i	0.0610185	+	0.0610185i
$584$			170.374i			0.291736i
$585$	180.292	+	23.4226i	0.308191	+	0.0400386i
$586$	676.981			1.15526
$587$	−283.065	+	283.065i	−0.482224	+	0.482224i	−0.905841	−	0.423617i	$-0.860760\pi$
$587$	−283.065	+	283.065i	−0.482224	+	0.482224i	0.423617	+	0.905841i	$0.360760\pi$
$588$	−52.1017	−	52.1017i	−0.0886083	−	0.0886083i
$589$		−	1069.45i		−	1.81571i
$590$	−118.671	+	913.451i	−0.201137	+	1.54822i
$591$	301.499			0.510150
$592$	111.271	−	111.271i	0.187957	−	0.187957i
$593$	5.75309	+	5.75309i	0.00970167	+	0.00970167i	0.711941	−	0.702239i	$-0.247816\pi$
$593$	5.75309	+	5.75309i	0.00970167	+	0.00970167i	−0.702239	+	0.711941i	$0.747816\pi$
$594$			65.1011i			0.109598i
$595$	255.010	−	196.369i	0.428588	−	0.330032i
$596$	1412.38			2.36976
$597$	−33.9148	+	33.9148i	−0.0568086	+	0.0568086i
$598$	−756.843	−	756.843i	−1.26562	−	1.26562i
$599$		−	619.287i		−	1.03387i	−0.856025	−	0.516934i	$-0.827073\pi$
$599$		−	619.287i		−	1.03387i	0.856025	−	0.516934i	$-0.172927\pi$
$600$	276.059	+	72.9597i	0.460098	+	0.121600i
$601$	457.367			0.761011			0.380505	−	0.924779i	$-0.375750\pi$
$601$	457.367			0.761011			0.380505	+	0.924779i	$0.375750\pi$
$602$	120.551	−	120.551i	0.200251	−	0.200251i
$603$	−63.6174	−	63.6174i	−0.105502	−	0.105502i
$604$		−	1038.79i		−	1.71985i
$605$	321.603	+	417.642i	0.531575	+	0.690317i
$606$	−990.383			−1.63430
$607$	−25.5979	+	25.5979i	−0.0421713	+	0.0421713i	−0.727878	−	0.685707i	$-0.759493\pi$
$607$	−25.5979	+	25.5979i	−0.0421713	+	0.0421713i	0.685707	+	0.727878i	$0.259493\pi$
$608$	639.356	+	639.356i	1.05157	+	1.05157i
$609$		−	80.4606i		−	0.132119i
$610$	1405.58	+	182.606i	2.30423	+	0.299354i
$611$	663.961			1.08668
$612$	−313.657	+	313.657i	−0.512512	+	0.512512i
$613$	−308.221	−	308.221i	−0.502808	−	0.502808i	0.409501	−	0.912309i	$-0.365703\pi$
$613$	−308.221	−	308.221i	−0.502808	−	0.502808i	−0.912309	+	0.409501i	$0.865703\pi$
$614$		−	169.129i		−	0.275454i
$615$	25.0571	−	192.873i	0.0407433	−	0.313615i
$616$	−68.8567			−0.111780
$617$	21.2194	−	21.2194i	0.0343913	−	0.0343913i	−0.689702	−	0.724093i	$-0.742258\pi$
$617$	21.2194	−	21.2194i	0.0343913	−	0.0343913i	0.724093	+	0.689702i	$0.242258\pi$
$618$	755.332	+	755.332i	1.22222	+	1.22222i
$619$			794.043i			1.28278i	0.767213	+	0.641392i	$0.221643\pi$
$619$			794.043i			1.28278i	−0.767213	+	0.641392i	$0.778357\pi$
$620$	1056.28	−	813.380i	1.70367	−	1.31190i
$621$	144.548			0.232767
$622$	468.346	−	468.346i	0.752968	−	0.752968i
$623$	−41.5685	−	41.5685i	−0.0667230	−	0.0667230i
$624$			70.8721i			0.113577i
$625$	−543.389	−	308.794i	−0.869422	−	0.494071i
$626$	−112.432			−0.179603
$627$	−117.825	+	117.825i	−0.187919	+	0.187919i
$628$	−1214.69	−	1214.69i	−1.93423	−	1.93423i
$629$			1134.07i			1.80298i
$630$	−76.8641	−	99.8178i	−0.122007	−	0.158441i
$631$	−365.937			−0.579932			−0.289966	−	0.957037i	$-0.593644\pi$
$631$	−365.937			−0.579932			−0.289966	+	0.957037i	$0.593644\pi$
$632$	523.479	−	523.479i	0.828290	−	0.828290i
$633$	−210.087	−	210.087i	−0.331892	−	0.331892i
$634$			740.297i			1.16766i
$635$	−197.403	−	25.6457i	−0.310871	−	0.0403869i
$636$	134.177			0.210970
$637$	59.9931	−	59.9931i	0.0941808	−	0.0941808i
$638$	−155.548	−	155.548i	−0.243806	−	0.243806i
$639$		−	236.444i		−	0.370022i
$640$	−117.598	+	905.195i	−0.183747	+	1.41437i
$641$	610.251			0.952029			0.476014	−	0.879437i	$-0.342081\pi$
$641$	610.251			0.952029			0.476014	+	0.879437i	$0.342081\pi$
$642$	−562.230	+	562.230i	−0.875747	+	0.875747i
$643$	−18.4704	−	18.4704i	−0.0287253	−	0.0287253i	0.692598	−	0.721324i	$-0.256466\pi$
$643$	−18.4704	−	18.4704i	−0.0287253	−	0.0287253i	−0.721324	+	0.692598i	$0.756466\pi$
$644$			447.289i			0.694548i
$645$	139.281	−	107.253i	0.215940	−	0.166283i
$646$	−1882.66			−2.91433
$647$	−633.369	+	633.369i	−0.978931	+	0.978931i	−0.999783	−	0.0208512i	$-0.993362\pi$
$647$	−633.369	+	633.369i	−0.978931	+	0.978931i	0.0208512	+	0.999783i	$0.493362\pi$
$648$	41.9652	+	41.9652i	0.0647612	+	0.0647612i
$649$		−	229.041i		−	0.352914i
$650$	−245.782	+	929.969i	−0.378126	+	1.43072i
$651$	−201.054			−0.308839
$652$	−893.904	+	893.904i	−1.37102	+	1.37102i
$653$	345.393	+	345.393i	0.528933	+	0.528933i	0.920254	−	0.391321i	$-0.127982\pi$
$653$	345.393	+	345.393i	0.528933	+	0.528933i	−0.391321	+	0.920254i	$0.627982\pi$
$654$		−	321.473i		−	0.491548i
$655$	99.2852	+	128.934i	0.151580	+	0.196846i
$656$	75.8178			0.115576
$657$	54.8083	−	54.8083i	0.0834221	−	0.0834221i
$658$	−325.334	−	325.334i	−0.494428	−	0.494428i
$659$		−	347.238i		−	0.526917i	−0.964671	−	0.263458i	$-0.915137\pi$
$659$		−	347.238i		−	0.526917i	0.964671	−	0.263458i	$-0.0848632\pi$
$660$	−205.987	−	26.7608i	−0.312101	−	0.0405466i
$661$	−482.959			−0.730649			−0.365324	−	0.930880i	$-0.619042\pi$
$661$	−482.959			−0.730649			−0.365324	+	0.930880i	$0.619042\pi$
$662$	−728.166	+	728.166i	−1.09995	+	1.09995i
$663$	−361.165	−	361.165i	−0.544744	−	0.544744i
$664$			120.654i			0.181708i
$665$	41.5434	−	319.774i	0.0624713	−	0.480863i
$666$	443.907			0.666527
$667$	−345.374	+	345.374i	−0.517802	+	0.517802i
$668$	−265.184	−	265.184i	−0.396982	−	0.396982i
$669$			15.3639i			0.0229654i
$670$	377.144	−	290.418i	0.562902	−	0.433459i
$671$	−352.439			−0.525245
$672$	120.197	−	120.197i	0.178865	−	0.178865i
$673$	769.503	+	769.503i	1.14339	+	1.14339i	0.987825	+	0.155566i	$0.0497202\pi$
$673$	769.503	+	769.503i	1.14339	+	1.14339i	0.155566	+	0.987825i	$0.450280\pi$
$674$			121.882i			0.180834i
$675$	−65.3359	−	112.277i	−0.0967939	−	0.166337i
$676$	−134.276			−0.198633
$677$	265.615	−	265.615i	0.392341	−	0.392341i	−0.483180	−	0.875521i	$-0.660518\pi$
$677$	265.615	−	265.615i	0.392341	−	0.392341i	0.875521	+	0.483180i	$0.160518\pi$
$678$	218.939	+	218.939i	0.322918	+	0.322918i
$679$		−	339.154i		−	0.499490i
$680$	−489.425	−	635.580i	−0.719742	−	0.934676i
$681$	−380.606			−0.558893
$682$	−388.682	+	388.682i	−0.569916	+	0.569916i
$683$	346.533	+	346.533i	0.507369	+	0.507369i	0.913718	−	0.406349i	$-0.133198\pi$
$683$	346.533	+	346.533i	0.507369	+	0.507369i	−0.406349	+	0.913718i	$0.633198\pi$
$684$			444.414i			0.649728i
$685$	−1291.35	−	167.766i	−1.88518	−	0.244913i
$686$	−58.7920			−0.0857026
$687$	346.813	−	346.813i	0.504822	−	0.504822i
$688$	48.4559	+	48.4559i	0.0704301	+	0.0704301i
$689$			154.500i			0.224238i
$690$	−98.5275	+	758.400i	−0.142794	+	1.09913i
$691$	−330.788			−0.478709			−0.239355	−	0.970932i	$-0.576936\pi$
$691$	−330.788			−0.478709			−0.239355	+	0.970932i	$0.576936\pi$
$692$	−483.946	+	483.946i	−0.699343	+	0.699343i
$693$	22.1508	+	22.1508i	0.0319637	+	0.0319637i
$694$			0.845888i			0.00121886i
$695$	302.090	−	232.623i	0.434661	−	0.334709i
$696$	−200.538			−0.288129
$697$	−386.369	+	386.369i	−0.554331	+	0.554331i
$698$	−500.348	−	500.348i	−0.716830	−	0.716830i
$699$			45.5483i			0.0651620i
$700$	347.430	−	202.175i	0.496329	−	0.288821i
$701$	−595.747			−0.849853			−0.424926	−	0.905228i	$-0.639700\pi$
$701$	−595.747			−0.849853			−0.424926	+	0.905228i	$0.639700\pi$
$702$	−141.370	+	141.370i	−0.201382	+	0.201382i
$703$	803.421	+	803.421i	1.14285	+	1.14285i
$704$		−	411.440i		−	0.584432i
$705$	−289.446	−	375.882i	−0.410561	−	0.533165i
$706$	44.9098			0.0636116
$707$	−336.981	+	336.981i	−0.476635	+	0.476635i
$708$	−431.948	−	431.948i	−0.610097	−	0.610097i
$709$		−	546.791i		−	0.771215i	−0.922663	−	0.385608i	$-0.873992\pi$
$709$		−	546.791i		−	0.771215i	0.922663	−	0.385608i	$-0.126008\pi$
$710$	1240.55	+	161.166i	1.74725	+	0.226994i
$711$	−336.801			−0.473701
$712$	−103.604	+	103.604i	−0.145511	+	0.145511i
$713$	863.018	+	863.018i	1.21040	+	1.21040i
$714$			353.934i			0.495706i
$715$	30.8140	−	237.186i	0.0430965	−	0.331729i
$716$	1154.64			1.61262
$717$	−324.596	+	324.596i	−0.452714	+	0.452714i
$718$	1358.46	+	1358.46i	1.89201	+	1.89201i
$719$			383.796i			0.533791i	0.963725	+	0.266896i	$0.0859979\pi$
$719$			383.796i			0.533791i	−0.963725	+	0.266896i	$0.914002\pi$
$720$	40.1221	−	30.8958i	0.0557251	−	0.0429108i
$721$	514.008			0.712910
$722$	−523.413	+	523.413i	−0.724949	+	0.724949i
$723$	156.145	+	156.145i	0.215968	+	0.215968i
$724$		−	1174.61i		−	1.62239i
$725$	424.378	+	112.159i	0.585349	+	0.154702i
$726$	−579.655			−0.798422
$727$	−331.503	+	331.503i	−0.455988	+	0.455988i	−0.897336	−	0.441348i	$-0.854500\pi$
$727$	−331.503	+	331.503i	−0.455988	+	0.455988i	0.441348	+	0.897336i	$0.354500\pi$
$728$	−149.525	−	149.525i	−0.205392	−	0.205392i
$729$		−	27.0000i		−	0.0370370i
$730$	250.204	+	324.921i	0.342745	+	0.445097i
$731$	−493.864			−0.675600
$732$	−664.665	+	664.665i	−0.908012	+	0.908012i
$733$	771.577	+	771.577i	1.05263	+	1.05263i	0.998536	+	0.0540934i	$0.0172269\pi$
$733$	771.577	+	771.577i	1.05263	+	1.05263i	0.0540934	+	0.998536i	$0.482773\pi$
$734$		−	1165.14i		−	1.58739i
$735$	−60.1166	−	7.81004i	−0.0817913	−	0.0106259i
$736$	−1031.88			−1.40202
$737$	−83.6931	+	83.6931i	−0.113559	+	0.113559i
$738$	151.235	+	151.235i	0.204926	+	0.204926i
$739$			644.895i			0.872658i	0.899787	+	0.436329i	$0.143722\pi$
$739$			644.895i			0.872658i	−0.899787	+	0.436329i	$0.856278\pi$
$740$	−182.474	+	1404.57i	−0.246587	+	1.89807i
$741$	−511.726			−0.690589
$742$	75.7033	−	75.7033i	0.102026	−	0.102026i
$743$	351.711	+	351.711i	0.473366	+	0.473366i	0.903002	−	0.429636i	$-0.141358\pi$
$743$	351.711	+	351.711i	0.473366	+	0.473366i	−0.429636	+	0.903002i	$0.641358\pi$
$744$			501.102i			0.673525i
$745$	920.680	−	708.965i	1.23581	−	0.951631i
$746$	2006.22			2.68930
$747$	38.8139	−	38.8139i	0.0519597	−	0.0519597i
$748$	412.638	+	412.638i	0.551655	+	0.551655i
$749$			382.601i			0.510815i
$750$	633.620	−	266.266i	0.844826	−	0.355022i
$751$	1346.30			1.79268			0.896339	−	0.443369i	$-0.146217\pi$
$751$	1346.30			1.79268			0.896339	+	0.443369i	$0.146217\pi$
$752$	130.769	−	130.769i	0.173895	−	0.173895i
$753$	39.1329	+	39.1329i	0.0519693	+	0.0519693i
$754$		−	675.560i		−	0.895968i
$755$	−521.436	−	677.151i	−0.690644	−	0.896888i
$756$	83.5485			0.110514
$757$	391.030	−	391.030i	0.516553	−	0.516553i	−0.399974	−	0.916527i	$-0.630981\pi$
$757$	391.030	−	391.030i	0.516553	−	0.516553i	0.916527	+	0.399974i	$0.130981\pi$
$758$	114.748	+	114.748i	0.151383	+	0.151383i
$759$		−	190.163i		−	0.250545i
$760$	−796.996	−	103.542i	−1.04868	−	0.136239i
$761$	−385.783			−0.506943			−0.253471	−	0.967343i	$-0.581572\pi$
$761$	−385.783			−0.506943			−0.253471	+	0.967343i	$0.581572\pi$
$762$	154.788	−	154.788i	0.203133	−	0.203133i
$763$	−109.382	−	109.382i	−0.143358	−	0.143358i
$764$		−	1434.61i		−	1.87776i
$765$	−47.0173	+	361.908i	−0.0614605	+	0.473083i
$766$	1819.75			2.37565
$767$	497.373	−	497.373i	0.648465	−	0.648465i
$768$	−199.066	−	199.066i	−0.259201	−	0.259201i
$769$			1014.63i			1.31941i	0.751525	+	0.659705i	$0.229319\pi$
$769$			1014.63i			1.31941i	−0.751525	+	0.659705i	$0.770681\pi$
$770$	−131.317	+	101.120i	−0.170542	+	0.131325i
$771$	−338.977			−0.439659
$772$	771.776	−	771.776i	0.999710	−	0.999710i
$773$	−833.644	−	833.644i	−1.07845	−	1.07845i	−0.996648	−	0.0818044i	$-0.973932\pi$
$773$	−833.644	−	833.644i	−1.07845	−	1.07845i	−0.0818044	−	0.996648i	$-0.526068\pi$
$774$			193.312i			0.249757i
$775$	280.262	−	1060.43i	0.361628	−	1.36830i
$776$	−845.299			−1.08930
$777$	151.041	−	151.041i	0.194390	−	0.194390i
$778$	106.187	+	106.187i	0.136488	+	0.136488i
$779$			547.437i			0.702743i
$780$	−389.197	−	505.421i	−0.498970	−	0.647976i
$781$	−311.058			−0.398282
$782$	1519.25	−	1519.25i	1.94277	−	1.94277i
$783$	64.5120	+	64.5120i	0.0823909	+	0.0823909i
$784$		−	23.6316i		−	0.0301424i
$785$	−1401.55	−	182.083i	−1.78542	−	0.231953i
$786$	−178.951			−0.227673
$787$	−204.794	+	204.794i	−0.260221	+	0.260221i	−0.825144	−	0.564923i	$-0.808906\pi$
$787$	−204.794	+	204.794i	−0.260221	+	0.260221i	0.564923	+	0.825144i	$0.308906\pi$
$788$	−748.028	−	748.028i	−0.949274	−	0.949274i
$789$		−	564.573i		−	0.715555i
$790$	229.572	−	1767.09i	0.290597	−	2.23683i
$791$	148.989			0.188355
$792$	55.2082	−	55.2082i	0.0697073	−	0.0697073i
$793$	−765.337	−	765.337i	−0.965116	−	0.965116i
$794$			1520.80i			1.91537i
$795$	87.4655	−	67.3523i	0.110019	−	0.0847199i
$796$	168.287			0.211416
$797$	−813.821	+	813.821i	−1.02111	+	1.02111i	−0.0213333	+	0.999772i	$0.506791\pi$
$797$	−813.821	+	813.821i	−1.02111	+	1.02111i	−0.999772	+	0.0213333i	$0.993209\pi$
$798$	250.740	+	250.740i	0.314211	+	0.314211i
$799$			1332.80i			1.66809i
$800$	466.412	+	801.512i	0.583015	+	1.00189i
$801$	66.6578			0.0832183
$802$	790.056	−	790.056i	0.985108	−	0.985108i
$803$	−72.1041	−	72.1041i	−0.0897934	−	0.0897934i
$804$			315.674i			0.392629i
$805$	224.524	+	291.572i	0.278912	+	0.362202i
$806$	−1688.08			−2.09439
$807$	407.440	−	407.440i	0.504882	−	0.504882i
$808$	839.883	+	839.883i	1.03946	+	1.03946i
$809$		−	288.800i		−	0.356984i	−0.983941	−	0.178492i	$-0.942878\pi$
$809$		−	288.800i		−	0.356984i	0.983941	−	0.178492i	$-0.0571219\pi$
$810$	141.661	+	18.4038i	0.174890	+	0.0227208i
$811$	929.694			1.14635			0.573177	−	0.819431i	$-0.305711\pi$
$811$	929.694			1.14635			0.573177	+	0.819431i	$0.305711\pi$
$812$	−199.625	+	199.625i	−0.245844	+	0.245844i
$813$	−310.747	−	310.747i	−0.382223	−	0.382223i
$814$		−	583.991i		−	0.717433i
$815$	−133.996	+	1031.42i	−0.164413	+	1.26554i
$816$	−142.265			−0.174344
$817$	−349.872	+	349.872i	−0.428240	+	0.428240i
$818$	−77.9155	−	77.9155i	−0.0952512	−	0.0952512i
$819$			96.2031i			0.117464i
$820$	−540.692	+	416.357i	−0.659380	+	0.507752i
$821$	−257.969			−0.314214			−0.157107	−	0.987582i	$-0.550217\pi$
$821$	−257.969			−0.314214			−0.157107	+	0.987582i	$0.550217\pi$
$822$	1012.57	−	1012.57i	1.23184	−	1.23184i
$823$	−1099.78	−	1099.78i	−1.33631	−	1.33631i	−0.899606	−	0.436703i	$-0.856146\pi$
$823$	−1099.78	−	1099.78i	−1.33631	−	1.33631i	−0.436703	−	0.899606i	$-0.643854\pi$
$824$		−	1281.10i		−	1.55473i
$825$	−147.709	+	85.9539i	−0.179041	+	0.104187i
$826$	−487.415			−0.590091
$827$	145.623	−	145.623i	0.176086	−	0.176086i	−0.613561	−	0.789647i	$-0.710264\pi$
$827$	145.623	−	145.623i	0.176086	−	0.176086i	0.789647	+	0.613561i	$0.210264\pi$
$828$	−358.629	−	358.629i	−0.433127	−	0.433127i
$829$		−	1281.05i		−	1.54530i	−0.634835	−	0.772648i	$-0.718932\pi$
$829$		−	1281.05i		−	1.54530i	0.634835	−	0.772648i	$-0.281068\pi$
$830$	177.188	+	230.101i	0.213479	+	0.277230i
$831$	618.475			0.744254
$832$	893.460	−	893.460i	1.07387	−	1.07387i
$833$	120.427	+	120.427i	0.144570	+	0.144570i
$834$			419.277i			0.502731i
$835$	−305.978	−	39.7511i	−0.366441	−	0.0476061i
$836$	584.657			0.699351
$837$	161.202	−	161.202i	0.192595	−	0.192595i
$838$	−1172.48	−	1172.48i	−1.39915	−	1.39915i
$839$		−	303.598i		−	0.361858i	−0.983496	−	0.180929i	$-0.942090\pi$
$839$		−	303.598i		−	0.361858i	0.983496	−	0.180929i	$-0.0579103\pi$
$840$	−19.4655	+	149.833i	−0.0231733	+	0.178373i
$841$	532.718			0.633434
$842$	337.461	−	337.461i	0.400785	−	0.400785i
$843$	−3.99909	−	3.99909i	−0.00474388	−	0.00474388i
$844$			1042.47i			1.23515i
$845$	−87.5298	+	67.4019i	−0.103586	+	0.0797656i
$846$	521.695			0.616661
$847$	−197.229	+	197.229i	−0.232856	+	0.232856i
$848$	30.4292	+	30.4292i	0.0358835	+	0.0358835i
$849$			150.951i			0.177799i
$850$	−1866.77	−	493.370i	−2.19620	−	0.580436i
$851$	−1296.67			−1.52371
$852$	−586.625	+	586.625i	−0.688527	+	0.688527i
$853$	39.5202	+	39.5202i	0.0463309	+	0.0463309i	0.729893	−	0.683562i	$-0.239570\pi$
$853$	39.5202	+	39.5202i	0.0463309	+	0.0463309i	−0.683562	+	0.729893i	$0.739570\pi$
$854$			750.014i			0.878237i
$855$	223.081	+	289.698i	0.260913	+	0.338829i
$856$	953.584			1.11400
$857$	388.871	−	388.871i	0.453758	−	0.453758i	−0.442842	−	0.896600i	$-0.646030\pi$
$857$	388.871	−	388.871i	0.453758	−	0.453758i	0.896600	+	0.442842i	$0.146030\pi$
$858$	185.982	+	185.982i	0.216762	+	0.216762i
$859$			375.068i			0.436633i	0.975878	+	0.218317i	$0.0700565\pi$
$859$			375.068i			0.436633i	−0.975878	+	0.218317i	$0.929943\pi$
$860$	−611.659	−	79.4636i	−0.711231	−	0.0923996i
$861$	102.917			0.119531
$862$	−370.647	+	370.647i	−0.429985	+	0.429985i
$863$	−374.656	−	374.656i	−0.434132	−	0.434132i	0.455899	−	0.890031i	$-0.349318\pi$
$863$	−374.656	−	374.656i	−0.434132	−	0.434132i	−0.890031	+	0.455899i	$0.849318\pi$
$864$			192.744i			0.223084i
$865$	−72.5435	+	558.392i	−0.0838653	+	0.645540i
$866$	−780.236			−0.900966
$867$	371.033	−	371.033i	0.427951	−	0.427951i
$868$	498.822	+	498.822i	0.574680	+	0.574680i
$869$			443.085i			0.509880i
$870$	−382.448	+	294.502i	−0.439595	+	0.338508i
$871$	−363.487			−0.417321
$872$	−272.621	+	272.621i	−0.312639	+	0.312639i
$873$	271.928	+	271.928i	0.311487	+	0.311487i
$874$		−	2152.59i		−	2.46291i
$875$	124.993	−	306.189i	0.142849	−	0.349930i
$876$	−271.962			−0.310459
$877$	281.962	−	281.962i	0.321507	−	0.321507i	−0.527838	−	0.849345i	$-0.676997\pi$
$877$	281.962	−	281.962i	0.321507	−	0.321507i	0.849345	+	0.527838i	$0.176997\pi$
$878$	−314.899	−	314.899i	−0.358654	−	0.358654i
$879$			369.374i			0.420220i
$880$	−40.6456	−	52.7834i	−0.0461881	−	0.0599811i
$881$	−950.305			−1.07867			−0.539333	−	0.842092i	$-0.681324\pi$
$881$	−950.305			−1.07867			−0.539333	+	0.842092i	$0.681324\pi$
$882$	47.1385	−	47.1385i	0.0534450	−	0.0534450i
$883$	−891.004	−	891.004i	−1.00907	−	1.00907i	−0.999959	−	0.00910653i	$-0.997101\pi$
$883$	−891.004	−	891.004i	−1.00907	−	1.00907i	−0.00910653	−	0.999959i	$-0.502899\pi$
$884$			1792.12i			2.02729i
$885$	−498.396	−	64.7491i	−0.563159	−	0.0731628i
$886$	2461.06			2.77772
$887$	316.251	−	316.251i	0.356540	−	0.356540i	−0.505996	−	0.862536i	$-0.668875\pi$
$887$	316.251	−	316.251i	0.356540	−	0.356540i	0.862536	+	0.505996i	$0.168875\pi$
$888$	−376.450	−	376.450i	−0.423930	−	0.423930i
$889$		−	105.334i		−	0.118486i
$890$	−45.4356	+	349.733i	−0.0510512	+	0.392959i
$891$	−35.5204			−0.0398657
$892$	38.1182	−	38.1182i	0.0427334	−	0.0427334i
$893$	944.208	+	944.208i	1.05734	+	1.05734i
$894$			1277.83i			1.42934i
$895$	752.670	−	579.589i	0.840972	−	0.647586i
$896$	−483.009			−0.539073
$897$	412.948	−	412.948i	0.460366	−	0.460366i
$898$	1557.30	+	1557.30i	1.73419	+	1.73419i
$899$			770.331i			0.856876i
$900$	−116.463	+	440.664i	−0.129404	+	0.489627i
$901$	−310.135			−0.344212
$902$	198.961	−	198.961i	0.220577	−	0.220577i
$903$	65.7749	+	65.7749i	0.0728405	+	0.0728405i
$904$		−	371.336i		−	0.410770i
$905$	−589.613	−	765.687i	−0.651506	−	0.846063i
$906$	939.833			1.03734
$907$	−407.150	+	407.150i	−0.448897	+	0.448897i	−0.894988	−	0.446091i	$-0.852816\pi$
$907$	−407.150	+	407.150i	−0.448897	+	0.448897i	0.446091	+	0.894988i	$0.352816\pi$
$908$	944.295	+	944.295i	1.03997	+	1.03997i
$909$		−	540.372i		−	0.594468i
$910$	−504.748	−	65.5743i	−0.554668	−	0.0720597i
$911$	637.398			0.699668			0.349834	−	0.936812i	$-0.386238\pi$
$911$	637.398			0.699668			0.349834	+	0.936812i	$0.386238\pi$
$912$	−100.786	+	100.786i	−0.110511	+	0.110511i
$913$	−51.0623	−	51.0623i	−0.0559281	−	0.0559281i
$914$		−	1471.04i		−	1.60945i
$915$	−99.6333	+	766.912i	−0.108889	+	0.838155i
$916$	−1720.91			−1.87872
$917$	−60.8886	+	60.8886i	−0.0663998	+	0.0663998i
$918$	−283.779	−	283.779i	−0.309127	−	0.309127i
$919$			1104.07i			1.20138i	0.799483	+	0.600689i	$0.205107\pi$
$919$			1104.07i			1.20138i	−0.799483	+	0.600689i	$0.794893\pi$
$920$	726.707	−	559.597i	0.789899	−	0.608258i
$921$	92.2800			0.100195
$922$	209.091	−	209.091i	0.226780	−	0.226780i
$923$	−675.477	−	675.477i	−0.731828	−	0.731828i
$924$		−	109.914i		−	0.118954i
$925$	586.097	+	1007.19i	0.633618	+	1.08885i
$926$	−2238.40			−2.41727
$927$	−412.123	+	412.123i	−0.444577	+	0.444577i
$928$	−460.531	−	460.531i	−0.496261	−	0.496261i
$929$		−	1765.37i		−	1.90029i	−0.311814	−	0.950143i	$-0.600937\pi$
$929$		−	1765.37i		−	1.90029i	0.311814	−	0.950143i	$-0.399063\pi$
$930$	735.898	+	955.657i	0.791288	+	1.02759i
$931$	170.630			0.183277
$932$	113.007	−	113.007i	0.121252	−	0.121252i
$933$	255.538	+	255.538i	0.273889	+	0.273889i
$934$			1383.88i			1.48167i
$935$	476.115	+	61.8545i	0.509214	+	0.0661546i
$936$	239.774			0.256169
$937$	867.153	−	867.153i	0.925457	−	0.925457i	−0.0719509	−	0.997408i	$-0.522923\pi$
$937$	867.153	−	867.153i	0.925457	−	0.925457i	0.997408	+	0.0719509i	$0.0229225\pi$
$938$	178.105	+	178.105i	0.189877	+	0.189877i
$939$		−	61.3448i		−	0.0653299i
$940$	−214.450	+	1650.70i	−0.228139	+	1.75606i
$941$	−1390.62			−1.47781			−0.738907	−	0.673807i	$-0.764658\pi$
$941$	−1390.62			−1.47781			−0.738907	+	0.673807i	$0.764658\pi$
$942$	1098.98	−	1098.98i	1.16665	−	1.16665i
$943$	−441.765	−	441.765i	−0.468468	−	0.468468i
$944$		−	195.918i		−	0.207540i
$945$	54.4625	−	41.9385i	0.0576322	−	0.0443794i
$946$	254.315			0.268832
$947$	−55.6539	+	55.6539i	−0.0587686	+	0.0587686i	−0.735880	−	0.677112i	$-0.763231\pi$
$947$	−55.6539	+	55.6539i	−0.0587686	+	0.0587686i	0.677112	+	0.735880i	$0.263231\pi$
$948$	835.614	+	835.614i	0.881450	+	0.881450i
$949$		−	313.154i		−	0.329984i
$950$	−1672.02	+	972.971i	−1.76002	+	1.02418i
$951$	−403.920			−0.424732
$952$	300.150	−	300.150i	0.315283	−	0.315283i
$953$	222.327	+	222.327i	0.233292	+	0.233292i	0.814065	−	0.580773i	$-0.197250\pi$
$953$	222.327	+	222.327i	0.233292	+	0.233292i	−0.580773	+	0.814065i	$0.697250\pi$
$954$			121.395i			0.127249i
$955$	−720.126	−	935.174i	−0.754058	−	0.979240i
$956$	1610.66			1.68479
$957$	84.8701	−	84.8701i	0.0886835	−	0.0886835i
$958$	−399.719	−	399.719i	−0.417243	−	0.417243i
$959$		−	689.060i		−	0.718519i
$960$	−895.298	−	116.313i	−0.932602	−	0.121159i
$961$	963.896			1.00301
$962$	1268.16	−	1268.16i	1.31825	−	1.31825i
$963$	−306.763	−	306.763i	−0.318549	−	0.318549i
$964$		−	774.800i		−	0.803735i
$965$	115.689	−	890.501i	0.119885	−	0.922798i
$966$	−404.680			−0.418924
$967$	807.256	−	807.256i	0.834805	−	0.834805i	−0.153365	−	0.988170i	$-0.549011\pi$
$967$	807.256	−	807.256i	0.834805	−	0.834805i	0.988170	+	0.153365i	$0.0490110\pi$
$968$	491.569	+	491.569i	0.507819	+	0.507819i
$969$		−	1027.21i		−	1.06008i
$970$	−1612.08	+	1241.37i	−1.66193	+	1.27976i
$971$	458.168			0.471852			0.235926	−	0.971771i	$-0.424188\pi$
$971$	458.168			0.471852			0.235926	+	0.971771i	$0.424188\pi$
$972$	−66.9878	+	66.9878i	−0.0689175	+	0.0689175i
$973$	142.660	+	142.660i	0.146619	+	0.146619i
$974$			1483.12i			1.52271i
$975$	−507.409	−	134.103i	−0.520419	−	0.137542i
$976$	−301.471			−0.308884
$977$	921.703	−	921.703i	0.943401	−	0.943401i	−0.0550806	−	0.998482i	$-0.517542\pi$
$977$	921.703	−	921.703i	0.943401	−	0.943401i	0.998482	+	0.0550806i	$0.0175416\pi$
$978$	−808.751	−	808.751i	−0.826944	−	0.826944i
$979$		−	87.6930i		−	0.0895741i
$980$	129.774	+	168.528i	0.132423	+	0.171967i
$981$	175.402			0.178799
$982$	−1637.21	+	1637.21i	−1.66722	+	1.66722i
$983$	398.575	+	398.575i	0.405468	+	0.405468i	0.880155	−	0.474687i	$-0.157439\pi$
$983$	398.575	+	398.575i	0.405468	+	0.405468i	−0.474687	+	0.880155i	$0.657439\pi$
$984$		−	256.506i		−	0.260677i
$985$	−863.099	−	112.129i	−0.876243	−	0.113837i
$986$	1356.08			1.37534
$987$	177.508	−	177.508i	0.179846	−	0.179846i
$988$	1269.61	+	1269.61i	1.28503	+	1.28503i
$989$		−	564.673i		−	0.570953i
$990$	24.2115	−	186.364i	0.0244561	−	0.188247i
$991$	861.216			0.869037			0.434519	−	0.900663i	$-0.356918\pi$
$991$	861.216			0.869037			0.434519	+	0.900663i	$0.356918\pi$
$992$	−1150.77	+	1150.77i	−1.16005	+	1.16005i
$993$	−397.301	−	397.301i	−0.400102	−	0.400102i
$994$			661.953i			0.665949i
$995$	109.701	−	84.4744i	0.110252	−	0.0848989i
$996$	−192.597			−0.193370
$997$	−1147.18	+	1147.18i	−1.15063	+	1.15063i	−0.164209	+	0.986426i	$0.552507\pi$
$997$	−1147.18	+	1147.18i	−1.15063	+	1.15063i	−0.986426	+	0.164209i	$0.947493\pi$
$998$	−865.811	−	865.811i	−0.867546	−	0.867546i
$999$			242.204i			0.242447i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.l.a.43.10	yes	24
3.2	odd	2		315.3.o.b.253.3		24
5.2	odd	4	inner	105.3.l.a.22.10	✓	24
5.3	odd	4		525.3.l.e.232.3		24
5.4	even	2		525.3.l.e.43.3		24
15.2	even	4		315.3.o.b.127.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.l.a.22.10	✓	24	5.2	odd	4	inner
105.3.l.a.43.10	yes	24	1.1	even	1	trivial
315.3.o.b.127.3		24	15.2	even	4
315.3.o.b.253.3		24	3.2	odd	2
525.3.l.e.43.3		24	5.4	even	2
525.3.l.e.232.3		24	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.24469 - 2.24469i) q^{2} +(1.22474 + 1.22474i) q^{3} -6.07726i q^{4} +(-3.05058 - 3.96156i) q^{5} +5.49834 q^{6} +(1.87083 - 1.87083i) q^{7} +(-4.66280 - 4.66280i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(2.24469 - 2.24469i) q^{2} +(1.22474 + 1.22474i) q^{3} -6.07726i q^{4} +(-3.05058 - 3.96156i) q^{5} +5.49834 q^{6} +(1.87083 - 1.87083i) q^{7} +(-4.66280 - 4.66280i) q^{8} +3.00000i q^{9} +(-15.7401 - 2.04487i) q^{10} +3.94671 q^{11} +(7.44309 - 7.44309i) q^{12} +(8.57045 + 8.57045i) q^{13} -8.39886i q^{14} +(1.11572 - 8.58808i) q^{15} +3.37595 q^{16} +(-17.2039 + 17.2039i) q^{17} +(6.73407 + 6.73407i) q^{18} +24.3758i q^{19} +(-24.0754 + 18.5392i) q^{20} +4.58258 q^{21} +(8.85913 - 8.85913i) q^{22} +(-19.6705 - 19.6705i) q^{23} -11.4215i q^{24} +(-6.38793 + 24.1701i) q^{25} +38.4760 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-11.3695 - 11.3695i) q^{28} -17.5580i q^{29} +(-16.7731 - 21.7820i) q^{30} -43.8736 q^{31} +(26.2292 - 26.2292i) q^{32} +(4.83371 + 4.83371i) q^{33} +77.2348i q^{34} +(-13.1185 - 1.70429i) q^{35} +18.2318 q^{36} +(32.9598 - 32.9598i) q^{37} +(54.7160 + 54.7160i) q^{38} +20.9932i q^{39} +(-4.24773 + 32.6962i) q^{40} +22.4582 q^{41} +(10.2865 - 10.2865i) q^{42} +(14.3533 + 14.3533i) q^{43} -23.9852i q^{44} +(11.8847 - 9.15174i) q^{45} -88.3085 q^{46} +(38.7355 - 38.7355i) q^{47} +(4.13468 + 4.13468i) q^{48} -7.00000i q^{49} +(39.9155 + 68.5933i) q^{50} -42.1407 q^{51} +(52.0849 - 52.0849i) q^{52} +(9.01352 + 9.01352i) q^{53} +16.4950i q^{54} +(-12.0397 - 15.6351i) q^{55} -17.4466 q^{56} +(-29.8541 + 29.8541i) q^{57} +(-39.4121 - 39.4121i) q^{58} -58.0335i q^{59} +(-52.1920 - 6.78052i) q^{60} -89.2995 q^{61} +(-98.4827 + 98.4827i) q^{62} +(5.61249 + 5.61249i) q^{63} -104.249i q^{64} +(7.80752 - 60.0972i) q^{65} +21.7004 q^{66} +(-21.2058 + 21.2058i) q^{67} +(104.552 + 104.552i) q^{68} -48.1828i q^{69} +(-33.2726 + 25.6214i) q^{70} -78.8147 q^{71} +(13.9884 - 13.9884i) q^{72} +(-18.2694 - 18.2694i) q^{73} -147.969i q^{74} +(-37.4258 + 21.7786i) q^{75} +148.138 q^{76} +(7.38362 - 7.38362i) q^{77} +(47.1233 + 47.1233i) q^{78} +112.267i q^{79} +(-10.2986 - 13.3740i) q^{80} -9.00000 q^{81} +(50.4118 - 50.4118i) q^{82} +(-12.9380 - 12.9380i) q^{83} -27.8495i q^{84} +(120.636 + 15.6724i) q^{85} +64.4373 q^{86} +(21.5040 - 21.5040i) q^{87} +(-18.4027 - 18.4027i) q^{88} -22.2193i q^{89} +(6.13461 - 47.2202i) q^{90} +32.0677 q^{91} +(-119.543 + 119.543i) q^{92} +(-53.7340 - 53.7340i) q^{93} -173.898i q^{94} +(96.5661 - 74.3602i) q^{95} +64.2481 q^{96} +(90.6427 - 90.6427i) q^{97} +(-15.7128 - 15.7128i) q^{98} +11.8401i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 16 q^{5} + 24 q^{6} - 48 q^{8}+O(q^{10}) \) 24 * q + 8 * q^2 + 16 * q^5 + 24 * q^6 - 48 * q^8	\( 24 q + 8 q^{2} + 16 q^{5} + 24 q^{6} - 48 q^{8} - 40 q^{10} - 48 q^{12} + 64 q^{13} - 184 q^{16} + 24 q^{17} + 24 q^{18} + 72 q^{20} + 8 q^{22} + 8 q^{23} - 136 q^{25} - 80 q^{26} + 96 q^{30} + 96 q^{31} + 56 q^{32} - 72 q^{33} + 168 q^{36} + 8 q^{37} + 56 q^{38} + 232 q^{40} + 320 q^{41} - 112 q^{43} - 72 q^{45} + 320 q^{46} + 64 q^{47} + 192 q^{48} - 256 q^{50} - 192 q^{51} + 96 q^{52} - 72 q^{53} - 80 q^{55} - 336 q^{56} + 48 q^{57} - 512 q^{58} - 192 q^{60} - 496 q^{61} - 776 q^{62} + 312 q^{65} - 192 q^{66} - 192 q^{67} + 568 q^{68} + 112 q^{70} - 144 q^{71} + 144 q^{72} + 224 q^{73} + 144 q^{75} + 416 q^{76} + 112 q^{77} - 216 q^{78} - 528 q^{80} - 216 q^{81} + 352 q^{82} - 32 q^{83} + 24 q^{85} + 240 q^{86} + 384 q^{87} + 216 q^{88} - 24 q^{90} + 1304 q^{92} + 376 q^{95} + 168 q^{96} - 816 q^{97} - 56 q^{98}+O(q^{100}) \) 24 * q + 8 * q^2 + 16 * q^5 + 24 * q^6 - 48 * q^8 - 40 * q^10 - 48 * q^12 + 64 * q^13 - 184 * q^16 + 24 * q^17 + 24 * q^18 + 72 * q^20 + 8 * q^22 + 8 * q^23 - 136 * q^25 - 80 * q^26 + 96 * q^30 + 96 * q^31 + 56 * q^32 - 72 * q^33 + 168 * q^36 + 8 * q^37 + 56 * q^38 + 232 * q^40 + 320 * q^41 - 112 * q^43 - 72 * q^45 + 320 * q^46 + 64 * q^47 + 192 * q^48 - 256 * q^50 - 192 * q^51 + 96 * q^52 - 72 * q^53 - 80 * q^55 - 336 * q^56 + 48 * q^57 - 512 * q^58 - 192 * q^60 - 496 * q^61 - 776 * q^62 + 312 * q^65 - 192 * q^66 - 192 * q^67 + 568 * q^68 + 112 * q^70 - 144 * q^71 + 144 * q^72 + 224 * q^73 + 144 * q^75 + 416 * q^76 + 112 * q^77 - 216 * q^78 - 528 * q^80 - 216 * q^81 + 352 * q^82 - 32 * q^83 + 24 * q^85 + 240 * q^86 + 384 * q^87 + 216 * q^88 - 24 * q^90 + 1304 * q^92 + 376 * q^95 + 168 * q^96 - 816 * q^97 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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